Precalculus 10th Edition Larson Test Bank

Section 1.10 - Mathematical Modeling and Variation

Copyright Cengage Learning. Powered by Cognero.

1. Assume that y is directly proportional to x. Use the given x-value and y-value to find a linear model that relates y and x.

a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 3.5.35

QUESTION TYPE: Multi-Mode (Multiple choice)

HAS VARIABLES: True

DATE CREATED: 6/10/2014 4:21 PM

DATE MODIFIED: 10/7/2014 5:48 AM


a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 3.5.36


HAS VARIABLES: True




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a. y = x

b. y = – 2400x

c. y = x

d. y = – x

e. y = – x

ANSWER: a

POINTS: 1

REFERENCES: 3.5.37


HAS VARIABLES: True



4. The simple interest on an investment is directly proportional to the amount of the investment. By investing $2400 in a certain bond issue, you obtained an interest payment of $111.75 after 1 year. Find a mathematical model that gives the interest I for this bond issue after 1 year in terms of the amount invested P. (Round your answer to three decimal places.)

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 3.5.39


HAS VARIABLES: True



5. The simple interest on an investment is directly proportional to the amount of the investment. By investing $5800 in a municipal bond, you obtained an interest payment of $221.25 after 1 year. Find a mathematical model that gives the interest I for this municipal bond after 1 year in terms of the amount invested P. (Round your answer to three decimal places.)

a.

b.

c.

d.



e.

ANSWER: c

POINTS: 1

REFERENCES: 3.5.40


HAS VARIABLES: True



6. On a yardstick with scales in inches and centimeters, you notice that 11 inches is approximately the same length as 33 centimeters. Use this information to find a mathematical model that relates centimeters y to inches x. Then use the model to find the numbers of centimeters in 60 inches and 70 inches. (Round your answer to one decimal place.)

a. Model: y = x; 20 cm, 23.3 cm

b. Model: y = 3x; 180 cm, 23.3 cm

c. Model: y = 3x; 20 cm, 210 cm

d. Model: y = 3x; 180 cm, 210 cm

e. Model: y = x; 180 cm, 210 cm

ANSWER: d

POINTS: 1

REFERENCES: 3.5.41


HAS VARIABLES: True



7. When buying gasoline, you notice that 16 gallons of gasoline is approximately the same amount of gasoline as 51 liters. Use this information to find a linear model that relates liters y to gallons x. Then use the model to find the numbers of liters in 25 gallons and 45 gallons. (Round your answer to one decimal place.)

a. Model: y = x; 7.8 L, 14.1 L

b. Model: y = x; 79.7 L, 14.1 L

c. Model: y = x; 7.8 L, 143.4 L

d. Model: y = x; 79.7 L, 143.4 L

e. Model: y = x; 79.7 L, 143.4 L

ANSWER: d

POINTS: 1



REFERENCES: 3.5.42


HAS VARIABLES: True



8. Property tax is based on the assessed value of a property. A house that has an assessed value of $200,000 has a property tax of $4,820. Find a mathematical model that gives the amount of property tax y in terms of the assessed value x of the property. Use the model to find the property tax on a house that has an assessed value of $230,000. (Round your answer to four decimal places.)

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 3.5.43


HAS VARIABLES: True



9. State sales tax is based on retail price. An item that sells for $180.99 has a sales tax of $17.4. Find a mathematical model that gives the amount of sales tax y in terms of the retail price x. Use the model to find the sales tax on a $589.99 purchase. (Round your answer to four decimal places.)

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 3.5.44


HAS VARIABLES: True



10. A force of newtons stretches a spring meter (see figure).



How far will a force of 60 newtons stretch the spring? What force is required to stretch the spring 0.1 meter?

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 3.5.45


HAS VARIABLES: True



11. A force of 270 newtons stretches a spring 0.18 meter. What force is required to stretch the spring 0.19 meter?

a. 295 N

b. 290 N

c. 285 N

d. 280 N

e. 270 N

ANSWER: c

POINTS: 1

REFERENCES: 3.5.46


HAS VARIABLES: True



12. The coiled spring of a toy supports the weight of a child. The spring is compressed a distance of 1.6 inches by the weight of a 35-pound child. The toy will not work properly if its spring is compressed more than 6 inches. What is the weight of the heaviest child who should be allowed to use the toy? (Round your answer to



two decimal places.)

a. 136.25 lb

b. 126.25 lb

c. 131.25 lb

d. 35 lb

e. 141.25 lb

ANSWER: c

POINTS: 1

REFERENCES: 3.5.47


HAS VARIABLES: True



13. An overhead garage door has two springs, one on each side of the door (see figure). A force of pounds is required to stretch each spring 1 foot. Because of a pulley system, the springs stretch only one-half the distance

the door travels. The door moves a total of feet, and the springs are at their natural length when the door is open. Find the combined lifting force applied to the door by the springs when the door is closed.

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 3.5.48


HAS VARIABLES: True



14. Find a mathematical model representing the statement. (Determine the constant of proportionality.)



y is inversely proportional to x.

a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 3.5.69


HAS VARIABLES: True




y varies inversely as x.

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 3.5.68


HAS VARIABLES: True




z varies jointly as x and y.



a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 3.5.70


HAS VARIABLES: True




F is jointly proportional to r and the third power of s.

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 3.5.71


HAS VARIABLES: True




P varies directly as x and inversely as the square of y. (P = when x = 25 and y = 10.)



a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 3.5.72


HAS VARIABLES: True



19. The work W (in joules) done when lifting an object varies jointly with the mass m (in kilograms) of the object and the height h (in meters) that the object is lifted. The work done when a 120-kilogram object is lifted 1.8 meters is 2116.8 joules. How much work is done when lifting a 200-kilogram object 1.5 meters?

a. 2960 J

b. 2920 J

c. 2940 J

d. 2950 J

e. 2930 J

ANSWER: c

POINTS: 1

REFERENCES: 3.5.79


HAS VARIABLES: True




a. y = 76x

b. y = – 76x

c. y = x



d. y = – x

e. y = – 380x

ANSWER: a

POINTS: 1

REFERENCES: 3.5.38


HAS VARIABLES: True



21. Determine whether the variation model is of the form or and find k. Then write a model that

relates y and x.

x 4 8 12 16 20

y 1

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 3.5.31


HAS VARIABLES: True




relates y and x.

x 9 18 27 36 45

y 2 4 6 8 10

a.



b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 3.5.32


HAS VARIABLES: True




relates y and x.

x 5 10 15 20 25

y –1.5 –3 –4.5 –6 –7.5

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 3.5.33


HAS VARIABLES: True






relates y and x.

x 5 10 15 20 25

y 26 13

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 3.5.34


HAS VARIABLES: True



25. Use the given value of k to complete the table for the direct variation model

.

Plot the points on a rectangular coordinate system.

x 8 10 12 14 16

a.

x 8 10 12 14 16

256 196 144 100 64



b.

x 8 10 12 14 16

64 100 144 196 256

c.

x 8 10 12 14 16

64 64 64 64 64



d.

x 8 10 12 14 16

64 100 144 100 64

e.

x 8 10 12 14 16

8 10 12 14 16



ANSWER: b

POINTS: 1

REFERENCES: 3.5.23


HAS VARIABLES: True

DATE CREATED: 10/22/2014 11:56 PM

DATE MODIFIED: 5/18/2015 11:41 PM


.


x 8 10 12 14 16

a.

x 8 10 12 14 16

128 200 288 392 512



b.

x 8 10 12 14 16

8 10 12 14 16

c.

x 8 10 12 14 16

128 128 128 128 128



d.

x 8 10 12 14 16

512 392 288 200 128

e.

x 8 10 12 14 16

128 200 288 200 128



ANSWER: a

POINTS: 1

REFERENCES: 3.5.24


HAS VARIABLES: True

DATE CREATED: 10/22/2014 11:38 PM



.


x 8 10 12 14 16

a.

x 8 10 12 14 16

32 50 72 98 128



b.

x 8 10 12 14 16

8 10 12 14 16

c.

x 8 10 12 14 16

32 32 32 32 32



d.

x 8 10 12 14 16

128 98 72 50 32

e.

x 8 10 12 14 16

32 50 72 50 32



ANSWER: a

POINTS: 1

REFERENCES: 3.5.25


HAS VARIABLES: True

DATE CREATED: 10/22/2014 8:07 AM



.


x 8 10 12 14 16

a.

x 8 10 12 14 16

64 49 36 25 16



b.

x 8 10 12 14 16

16 16 16 16 16

c.

x 8 10 12 14 16

16 25 36 25 16



d.

x 8 10 12 14 16

16 25 36 49 64

e.

x 8 10 12 14 16

8 10 12 14 16



ANSWER: d

POINTS: 1

REFERENCES: 3.5.26


HAS VARIABLES: True



29. Use the given value of k to complete the table for the inverse variation model


x 2 4 6 8 10

k = 2

a.

x 2 4 6 8 10



b.

x 2 4 6 8 10

c.

x 2 4 6 8 10



d.

x 2 4 6 8 10

e.

x 2 4 6 8 10

2 4 6 8 10



ANSWER: a

POINTS: 1

REFERENCES: 3.5.27


HAS VARIABLES: True





x 8 10 12 14 16

k = 5

a.

x 8 10 12 14 16



b.

x 8 10 12 14 16

c.

x 8 10 12 14 16



d.

x 8 10 12 14 16

e.

x 8 10 12 14 16

8 10 12 14 16



ANSWER: a

POINTS: 1

REFERENCES: 3.5.28


HAS VARIABLES: True





x 4 6 8 10 12

k = 10

a.

x 4 6 8 10 12



b.

x 4 6 8 10 12

c.

x 4 6 8 10 12



d.

x 4 6 8 10 12

e.

x 4 6 8 10 12

4 6 8 10 12



ANSWER: a

POINTS: 1

REFERENCES: 3.5.29


HAS VARIABLES: True




.


x 8 10 12 14 16

k = 20

a.

x 8 10 12 14 16



b.

x 8 10 12 14 16

c.

x 8 10 12 14 16



d.

x 8 10 12 14 16

e.

x 8 10 12 14 16

8 10 12 14 16



ANSWER: a

POINTS: 1

REFERENCES: 3.5.30


HAS VARIABLES: True




z varies directly as the square of x and inversely as y. (z = 36 when x = 9 and y = 3.)

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 3.5.73


HAS VARIABLES: True






v varies jointly as p and q and inversely as the square of s. (ν = 1.4 when p = 4.4, q = 7.3 and s = 1.8.)

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 3.5.74


HAS VARIABLES: True



35. Use the fact that the diameter of the largest particle that can be moved by a stream varies approximately directly as the square of the velocity of the stream.

A stream with a velocity of mile per hour can move coarse sand particles about 0.07 inch in diameter.

Approximate the velocity required to carry particles 0.2 inch in diameter. (Round your answer to two decimal places.)

a. About 0.84 mi/h

b. About 0.19 mi/h

c. About –0.16 mi/h

d. About 0.49 mi/h

e. About 0.34 mi/h

ANSWER: e

POINTS: 1

REFERENCES: 3.5.75


HAS VARIABLES: True





36. Use the fact that the resistance of a wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area.

If #28 copper wire (which has a diameter of 0.0126 inch) has a resistance of 68.17 ohms per thousand feet, what length of #28 copper wire will produce a resistance of 30.5 ohms?

a. About 447 ft

b. About 442 ft

c. About 432 ft

d. About 452 ft

e. About 462 ft

ANSWER: a

POINTS: 1

REFERENCES: 3.5.77


HAS VARIABLES: True



37. Use the fact that the resistance of a wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area.

A 10-foot piece of copper wire produces a resistance of 0.2 ohm. Use the constant of proportionality k = 0.000833 to find the diameter of the wire.

(Round the answer up to three decimal places.)

a. 0.23 ft

b. 0.58 ft

c. 0.38 ft

d. 0.48 ft

e. 0.73 ft

ANSWER: a

POINTS: 1

REFERENCES: 3.5.78


HAS VARIABLES: True



38. The frequency of vibrations of a piano string varies directly as the square root of the tension on the string and inversely as the length of the string. The middle A string has a frequency of 430 vibrations per second. Find the frequency of a string that has 1.25 times as much tension and is 1.4 times as long.

a. 373.4 vibrations / sec

b. 343.4 vibrations / sec



c. 353.4 vibrations / sec

d. 383.4 vibrations / sec

e. 363.4 vibrations / sec

ANSWER: b

POINTS: 1

REFERENCES: 3.5.80


HAS VARIABLES: True



39. An oceanographer took readings of the water temperatures C (in degrees Celsius) at several depths d (in meters). The data collected are shown in the table.

Depth, d Temperature, C

1000 3.8°

2000 2.1°

3000 1.8°

4000 1.5°

5000 0.5°

Sketch a scatter plot of the data. a.

b.



c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 3.5.83a


HAS VARIABLES: True



40. Determine whether the variation model below is of the form or .

x 13 26 39 52 65

y 3 6 9 12 15



a.

b.

ANSWER: a

POINTS: 1

REFERENCES: 3.5.31


HAS VARIABLES: True



41. After determining whether the variation model below is of the form or , find the value of k.

x 154 161 168 175 182

y 66 69 72 75 78

a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 3.5.32


HAS VARIABLES: True



42. After determining whether the variation model below is of the form or , find the value of k.

x 20 40 60 80 100

y

a.

b.

c.



d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 3.5.33


HAS VARIABLES: True



43. Determine whether the variation model below is of the form or .

x 12 24 36 48 60

y

a. b.

ANSWER: b

POINTS: 1

REFERENCES: 3.5.34


HAS VARIABLES: True



44. Assume that y is directly proportional to x. If x = 28 and y = 21, determine a linear model that relates y and x. a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 3.5.36




HAS VARIABLES: True



45. The simple interest on an investment is directly proportional to the amount of the investment. By investing $6000 in a certain certificate of deposit, you obtained an interest payment of $276.00 after 1 year. Determine a mathematical model that gives the interest, I , for this CD after 1 year in terms of the amount invested, P.

a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 3.5.39


HAS VARIABLES: True



46. The sales tax on an item with a retail price of $972 is $68.04. Create a variational model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $82.62. a. $1182.28

b. $1151.92

c. $1180.29

d. $1192.52

e. $1124.60

ANSWER: c

POINTS: 1

REFERENCES: 3.5.44


HAS VARIABLES: True



47. Hooke's law states that the magnitude of force, F, required to stretch a spring x units beyond its natural length is directly proportional to x. If a force of 3 pounds stretches a spring from its natural length of 10 inches to a length of 10.7 inches, what force will stretch the spring to a length of 11.5 inches? Round your answer to the nearest hundredth. a.



b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 3.5.45b


HAS VARIABLES: True



48. Find a mathematical model for the verbal statement:

"Q is jointly proportional to the cube of h and the square root of m."

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 3.5.57


HAS VARIABLES: False



49. Find a mathematical model for the verbal statement: "m varies directly as the square of w and inversely as s."

a.

b.

c.

d.



e.

ANSWER: b

POINTS: 1

REFERENCES: 3.5.53


HAS VARIABLES: True



50. The electrical resistance, R, of a wire is directly proportional to its length, l, and inversely proportional to the square of its diameter, d. A wire 150 meters long of diameter 5 millimeters has a resistance of 12 ohms. Find the resistance of a wire made of the same material that has a diameter of 2 millimeters and is 24 meters long.

a. R = 14.5 ohms

b. R = 12 ohms

c. R = 15.8 ohms

d. R = 15.5 ohms

e. R = 0.083 ohms

ANSWER: b

POINTS: 1

REFERENCES: 3.5.77


HAS VARIABLES: True



Section 1.1 - Rectangular Coordinates

Copyright Cengage Learning. Powered by Cognero. Page 1

1. Approximate the coordinates of the points.

a. A: (4, 2), B: (–6, –6), C: (5, 2), D: (6, –5)

b. A: (1, 2), B: (–6, –6), C: (5, 2), D: (6, –5)

c. A: (2, 2), B: (–6, –6), C: (5, 2), D: (6, –5)

d. A: (3, 2), B: (–6, –6), C: (5, 2), D: (6, –5)

e. A: (–1, 2), B: (–6, –6), C: (5, 2), D: (6, –5)

ANSWER: e

POINTS: 1

REFERENCES: P.6.5

QUESTION TYPE: Multiple Choice

HAS VARIABLES: True



2. Find the coordinates of the point labeled II.



a. (-4, -3)

b. (-4, 3)

c. (3, 4)

d. (4, 3)

e. (-3, -4)

ANSWER: d

POINTS: 1

REFERENCES: P.6.6


HAS VARIABLES: True



3. Approximate the coordinates of the points.



a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: P.6.6


HAS VARIABLES: True



4. Which label corresponds to the coordinates (–3, –5)?



a. VI

b. VIII

c. V

d. VII

e. none

ANSWER: e

POINTS: 1

REFERENCES: P.6.7


HAS VARIABLES: True



5. Plot the points in the Cartesian plane.

(–4, 1), (–5, –2), (5, 4), (2, –4)

a. b.



c.

d.

e.



ANSWER: e

POINTS: 1

REFERENCES: P.6.7


HAS VARIABLES: True



6. Plot the points below whose coordinates are given on a Cartesian coordinate system.

(5, 2), (9, –6), (2, –4), (9, –5)

a.

b.



c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: P.6.8


HAS VARIABLES: True




(2, 6), (2.5, 6), (3, –6), (–6, 4.5)

a.

b.



c.

d.

e.



ANSWER: d

POINTS: 1

REFERENCES: P.6.9


HAS VARIABLES: True






a.

b.

c.

d.



e.

ANSWER: c

POINTS: 1

REFERENCES: P.6.10


HAS VARIABLES: True



9. A point is located six units to the left of the y-axis and seven units above the x-axis. Find the coordinates of the point.

a. (–6, 7)

b. (7, 6)

c. (–6, –7)

d. (6, –7)

e. (6, 7)

ANSWER: a

POINTS: 1

REFERENCES: P.6.11


HAS VARIABLES: True



10. Find the coordinates for the point that is four units to the left of the y-axis and is six units up from the x-axis. a. (-4, -6)

b. (4, -6)

c. (-4, 6)



d. (6, 6)

e. (4, 6)

ANSWER: c

POINTS: 1

REFERENCES: P.6.12


HAS VARIABLES: True



11. A point is located five units below the x-axis and the coordinates of the point are equal. Find the coordinates of the point.

a. (–5, 5)

b. (–5, 0)

c. (5, –5)

d. (–5, –5)

e. (5, 5)

ANSWER: d

POINTS: 1

REFERENCES: P.6.13


HAS VARIABLES: True



12. Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied.

x > 7 and y < 0

a. Quadrant I and IV

b. Quadrant III

c. Quadrant I

d. Quadrant IV

e. Quadrant II

ANSWER: d

POINTS: 1

REFERENCES: P.6.15


HAS VARIABLES: True




x < –8 and y < –6



a. Quadrant I

b. Quadrant I and II

c. Quadrant III

d. Quadrant II

e. Quadrant IV

ANSWER: c

POINTS: 1

REFERENCES: P.6.16


HAS VARIABLES: True




x = –2 and y > 0

a. Quadrant IV

b. Quadrant II or IV

c. Quadrant II

d. Quadrant I

e. Quadrant III

ANSWER: c

POINTS: 1

REFERENCES: P.6.17


HAS VARIABLES: True




x > 3 and y = 1

a. Quadrant III

b. Quadrant I

c. Quadrant III and IV

d. Quadrant II

e. Quadrant IV

ANSWER: b

POINTS: 1

REFERENCES: P.6.18


HAS VARIABLES: True






y < –6

a. Quadrant II or IV

b. Quadrant III or IV

c. Quadrant IV

d. Quadrant I

e. Quadrant II

ANSWER: b

POINTS: 1

REFERENCES: P.6.19


HAS VARIABLES: True




x < –9 and – y > 6

a. Quadrant I

b. Quadrant II

c. Quadrant IV

d. Quadrant III

e. Quadrant I or IV

ANSWER: d

POINTS: 1

REFERENCES: P.6.21


HAS VARIABLES: True



18. Determine the quadrant(s) in which (x, y) is located so that the conditions(s) is (are) satisfied.

– x > 6 and y < –2

a. Quadrant III

b. Quadrant I

c. Quadrant II

d. Quadrant I or IV

e. Quadrant IV



ANSWER: a

POINTS: 1

REFERENCES: P.6.22


HAS VARIABLES: True




xy < –4

a. Quadrant II or III

b. Quadrant I or III

c. Quadrant III or IV

d. Quadrant II or IV

e. Quadrant I or IV

ANSWER: d

POINTS: 1

REFERENCES: P.6.24


HAS VARIABLES: True



20. Sketch a scatter plot of the data shown in the table. The table shows the number y of Wal-Mart stores for each year x from 2000 through 2007.

Year, x Number of stores, y

2000 3700

2001 4400

2002 4680

2003 5010

2004 5550

2005 6360

2006 6680

2007 7340

a.

b.



x: Year (0 ↔ 2000)

y: Number of stores

x: Year (0 ↔ 2000)

y: Number of stores

c.

x: Year (0 ↔ 2000)

y: Number of stores

d.

x: Year (0 ↔ 2000)

y: Number of stores

e.



x: Year (0 ↔ 2000)

y: Number of stores

ANSWER: a

POINTS: 1

REFERENCES: P.6.25


HAS VARIABLES: True



21. Sketch a scatter plot of the data shown in the table. The table shows the lowest temperature on record y (in degrees Fahrenheit) in Duluth, Minnesota for each month x where x = 1 represents from January.

Months, x Temperature, y

1 –46

2 –36

3 –23

4 –7

5 14

6 25

7 31

8 42

9 24

10 3



11 –26

12 –15

a.

x: Months (1 ↔ January)

y: Temperature (in Fº)

b.



c.

d.







e.



ANSWER: a

POINTS: 1

REFERENCES: P.6.26


HAS VARIABLES: True



22. Find the distance between the two points (6, 1) and (6, 7). a. 1

b. 13

c. 12

d. 11

e. 6

ANSWER: e

POINTS: 1

REFERENCES: P.6.27


HAS VARIABLES: True





23. Find the distance between the two points (–3, –1) and (13, 29). a. 65

b. 68

c. 102

d. 31

e. 34

ANSWER: e

POINTS: 1

REFERENCES: P.6.28


HAS VARIABLES: True



24. Find the distance between the two points (10, 7) and (–5, 7).

a. 30

b. 20

c. 12

d. 40

e. 15

ANSWER: e

POINTS: 1

REFERENCES: P.6.29


HAS VARIABLES: True



25. Find the distance between the points.

(–8, –5), (–2, 3)

a. 10

b. 100

c. 2

d. 5

e. 8

ANSWER: a

POINTS: 1

REFERENCES: P.6.30




HAS VARIABLES: True



26. Find the distance between the points.

(–9, 4), (3, –5)

a. 4

b. 15

c. 9

d. 3

e. 225

ANSWER: b

POINTS: 1

REFERENCES: P.6.31


HAS VARIABLES: True



27. Find the distance between the points. (Round the answer to two decimal places)

(–6.5, 4.9), (–9.5, 7.5)

a. 15.76

b. 9.5

c. 7.5

d. 3.97

e. 6.5

ANSWER: d

POINTS: 1

REFERENCES: P.6.37


HAS VARIABLES: True



28. Find the distance between the points. (Round the answer to two decimal places)

(9.5, –4.1), (–3.3, 8.7)

a. 8.7

b. 9.5

c. 327.68

d. 3.3

e. 18.10



ANSWER: e

POINTS: 1

REFERENCES: P.6.38


HAS VARIABLES: True



29. Show that the points form the vertices of the indicated polygon.

Right triangle: (6, 2), (3, 4), (–3, –5)

a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: P.6.43


HAS VARIABLES: True



30. Given the points (–6, –8) and (4, –6). Find a third point so that the three points form the vertices of a right triangle.

a. (-16, 4)

b. (-11, 17)

c. (-6, -9)

d. (5, -6)

e. (4, 6)

ANSWER: b

POINTS: 1

REFERENCES: P.6.43


HAS VARIABLES: True






Right triangle: (3, 5), (5, 6), (6, 4)

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: P.6.44


HAS VARIABLES: True



32. Given points(–1,1), and (–11,–9) form the vertices of the base of a triangle, find a third point so that the three points form the vertices of an isosceles triangle.

a. (3, 1)

b. (4, -15)

c. (-15, -13)

d. (3, 5)

e. (-6, -4)

ANSWER: e

POINTS: 1

REFERENCES: P.6.45


HAS VARIABLES: True




Isosceles triangle: (7, –6), (9, 8), (–5, 6)

a. Distances between the points:

b. Distances between the points:

c. Distances between the points:

d. Distances between the points:



e. Distances between the points:

ANSWER: b

POINTS: 1

REFERENCES: P.6.45


HAS VARIABLES: True




Isosceles triangle: (7, 1), (5, 4), (2, 6)

a. Distances between the points:

b. Distances between the points:

c. Distances between the points:

d. Distances between the points:

e. Distances between the points:

ANSWER: b

POINTS: 1

REFERENCES: P.6.46


HAS VARIABLES: True



35. Plot the following points and find the distance between the points.

(11, 3), (5, 3)

a.

b.



Distance: 8 Distance: 6

c.

Distance: 9

d.

Distance: 10

e.



Distance: 7

ANSWER: b

POINTS: 1

REFERENCES: P.6.47


HAS VARIABLES: True



36. Plot the following points and find the midpoint of the line segment joining the points.

(9, 6), (5, 6)

a.

b.



Midpoint: (7, 6) Midpoint: (7, 6)

c.

Midpoint: (7, 6)

d.

Midpoint: (7, 6)

e.



Midpoint: (7, 6)

ANSWER: b

POINTS: 1

REFERENCES: P.6.48


HAS VARIABLES: True



37. Find the midpoint between the two points (–19, 9) and (11, 13).

a. (-15, 2)

b. (-15, 11)

c. (-8, 11)

d. (-4, 2)

e. (-4, 11)

ANSWER: e

POINTS: 1

REFERENCES: P.6.49c


HAS VARIABLES: True




(–5, 8), (7, 2)



a.

Distance:

b.

Distance:

c.

Distance:

d.

Distance:

e.



Distance:

ANSWER: d

POINTS: 1

REFERENCES: P.6.51


HAS VARIABLES: True




(3, 8), (8, 3)



a.

Distance:

b.

Distance:

c.

Distance:

d.

Distance:

e.



Distance:

ANSWER: e

POINTS: 1

REFERENCES: P.6.52


HAS VARIABLES: True



40. An airplane flies from one city in a straight line to another city, which is 360 kilometers north and 150 kilometers west of first city. How far does the plane fly?

a. 150 km

b. 390 km

c. 255 km

d. 360 km

e. 350 km

ANSWER: b

POINTS: 1

REFERENCES: P.6.57


HAS VARIABLES: True



41. A soccer player passes the ball from a point that is 13 yards from the end line and 16 yards from the sideline. The pass is received by a teammate who is 48 yards from the same end line and 39 yards from the same sideline, as shown in the figure. How long is the pass?



(a, b): (13, 16)

(c, d): (48, 39)

a. ≈ 44 yd

b. ≈ 43 yd

c. ≈ 45 yd

d. ≈ 42 yd

e. ≈ 46 yd

ANSWER: d

POINTS: 1

REFERENCES: P.6.58


HAS VARIABLES: True



42. A quarterback is standing in the middle of the field 41 yards from his goal line. He passes the ball to a player 8 yards to his left on the 26 yard line. How long was the pass?

a. 42 yards

b. 15 yards

c. 27 yards

d. 17 yards

e. 67 yards

ANSWER: d

POINTS: 1

REFERENCES: P.6.58


HAS VARIABLES: True



43. Use the Midpoint Formula to estimate the sales of Big Lots, Inc. in 2005, given the sales in 2003 and 2007.



Assume that the sales followed a linear pattern. Big Lots

Year Sales (in millions)

2003 4174

2007 4700

a. $4700 million

b. $4457 million

c. $4174 million

d. $4437 million

e. $4447 million

ANSWER: d

POINTS: 1

REFERENCES: P.6.59


HAS VARIABLES: True



44. Use the Midpoint Formula to estimate the sales of Dollar Tree Stores, Inc. in 2005, given the sales in 2003 and 2007. Assume that the sales followed a linear pattern. Dollar tree

Year Sales (in millions)

2003 2200

2007 4283

a. $3241.5 million

b. $3251.5 million

c. $3246.5 million

d. $3256.5 million

e. $3261.5 million

ANSWER: a

POINTS: 1

REFERENCES: P.6.60


HAS VARIABLES: True



45. Find the coordinates of the vertices of the polygon in its new position.

Original coordinates of vertices: (–5, –3), (–3, 6), (–5, –4), (–4, –7)

Shift: three units to the right, four units upward



a. (–2, 1), (0, 10), (–2, 0), (–1, –3)

b. (1, 1), (0, 10), (–2, 0), (–1, –3)

c. (2, 1), (0, 10), (–2, 0), (–1, –3)

d. (3, 1), (0, 10), (–2, 0), (–1, –3)

e. (4, 1), (0, 10), (–2, 0), (–1, –3)

ANSWER: a

POINTS: 1

REFERENCES: P.6.63


HAS VARIABLES: True



46. Find the coordinates of the vertices of the polygon in its new position.

Original coordinates of vertices: (6, 5), (3, 2), (4, 2), (5, 2)

Shift: six units downward, two units to the left

a. (13, –1), (1, –4), (2, –4), (3, –4)

b. (10, –1), (1, –4), (2, –4), (3, –4)

c. (12, –1), (1, –4), (2, –4), (3, –4)

d. (4, –1), (1, –4), (2, –4), (3, –4)

e. (11, –1), (1, –4), (2, –4), (3, –4)

ANSWER: d

POINTS: 1

REFERENCES: P.6.64


HAS VARIABLES: True



47. Use the graph, which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007.

Approximate the lowest price of a gallon of whole milk shown in the graph. When did this occur?

a. $2.97 / gal; 2001

b. $3.17 / gal; 2002



c. $3.07 / gal; 2003

d. $2.67 / gal; 1997

e. $3.87 / gal; 2004

ANSWER: d

POINTS: 1

REFERENCES: P.6.65


HAS VARIABLES: True



48. Use the graph, which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007.

Approximate the percent change in the price of milk from the price in 2000 to the highest price shown in the graph.

a. About 48%

b. About 58%

c. About 43%

d. About 53%

e. About 38%

ANSWER: e

POINTS: 1

REFERENCES: P.6.66


HAS VARIABLES: True



49. The graph shows the numbers of performers who were elected to the Rock and Roll Hall of Fame from 1991 through 2008. Describe any trends in the data. From these trends, predict the number of performers elected in 2009.



a. The number of performers elected in last four years in the graph seems to be nearly steady except for the first few years therefore five performers will be elected in 2009.

b. The number of performers elected in last four years in the graph seems to be nearly steady except for the first few years therefore seven performers will be elected in 2009.

c. The number of performers elected in last four years in the graph seems to be nearly steady except for the first few years therefore eight performers will be elected in 2009.

d. The number of performers elected in last four years in the graph seems to be nearly steady except for the first few years therefore six performers will be elected in 2009.

e. The number of performers elected in last four years in the graph seems to be nearly steady except for the first few years therefore nine performers will be elected in 2009.

ANSWER: a

POINTS: 1

REFERENCES: P.6.69


HAS VARIABLES: True



50. The Coca-Cola Company had sales of $19,999 million in 1999 and $29,511 million in 2007. Use the Midpoint Formula to estimate the sales in 2003. Assume that the sales followed a linear pattern.

a. $24,905 million

b. $24,855 million

c. $24,755 million

d. $24,955 million

e. $24,805 million

ANSWER: c

POINTS: 1

REFERENCES: P.6.71


HAS VARIABLES: True





51. Determine the quadrant(s) in which (x, y) is located so that the condition is satisfied. x = 2 and y < –8

a. quadrant II

b. quadrant IV

c. quadrants I and IV

d. quadrants II and IV

e. quadrants III and IV

ANSWER: b

POINTS: 1

REFERENCES: 11-20


HAS VARIABLES: True



52. Find the distance between the points. Round to the nearest hundredth, if necessary.

(–8, –8), (–1, 9)

a. 19.24

b. 7.07

c. 18.38

d. 10

e. 9.06

ANSWER: c

POINTS: 1

REFERENCES: 23-32


HAS VARIABLES: True



53. )Given points(5,–11), and (11,–5) form the vertices of the base of a triangle, find a third point so that the three points form the vertices of an isosceles triangle.

a. (8, -8)

b. (11, -12)

c. (6, -10)

d. (10, -6)

e. (10, -11)

ANSWER: a

POINTS: 1

REFERENCES: 37-44


HAS VARIABLES: True





54. Find the coordinates of the point C shown below.

a. (–2, 3) b. (3, -2)

c. (–4, –5) d. (-5, -4)

e. (–5, –2)

ANSWER: b

POINTS: 1


HAS VARIABLES: True



55. Plot the point (–3, 1) on the Cartesian plane.



a.

b.

c.

d.



e.

ANSWER: e

POINTS: 1


HAS VARIABLES: True



56. Find the coordinates of the point that is located 8 units below the x-axis and 3 units to the left of the y-axis.

a. (–8, –3) b. (8, –3)

c. (–3, 8) d. (3, –8)

e. (–3, –8)

ANSWER: e

POINTS: 1


HAS VARIABLES: True



57. Find the distance between the points (4, –3) and (11, –3).

a. 10 b.

c. 3 d.

e. 7

ANSWER: e

POINTS: 1




HAS VARIABLES: True



58. Find the distance between the points (4, –5) and (9, 0). Round the answer to the nearest tenth.

a. 7.1 b. 7.4

c. 7.3 d. 7.5

e. 6.9

ANSWER: a

POINTS: 1


HAS VARIABLES: True



59. Find the midpoint of the line segment joining the points (3, 6) and (9, –4).

a. (6, –10) b. (12, 2)

c. (6, 1) d. (–3, 5)

e. (3, –5)

ANSWER: c

POINTS: 1


HAS VARIABLES: True



60. Find the midpoint of the line segment joining the points (5.5, 4.3) and (13.6, –1.2).

a. (19.1, 3.1) b. (8.1, –5.5)

c. (–4.05, 2.75) d. (9.55, 1.55)

e. (4.05, –2.75)

ANSWER: d

POINTS: 1


HAS VARIABLES: True



61. Let M denote the midpoint of the line segment joining (4, 3) and (11, 6). Find the distance from M to the point (–6, –5). Round the answer to the nearest tenth.

a. 16.7 b. 16.1

c. 16.5 d. 15.9

e. 16.2



ANSWER: c

POINTS: 1


HAS VARIABLES: True



62. Let M denote the midpoint of the line segment joining (2, 3) and (7, 6). Find the midpoint between M and (–6, –4).

a. (2, 0.25) b. (–0.75, 0.25)

c. (–2, –0.5) d. (4.5, 4.5)

e. (0.5, 1)

ANSWER: b

POINTS: 1


HAS VARIABLES: True



63. Let S represent the midpoint between (5, 3) and (–5, –7). Let T represent the midpoint between (5, 3) and S. Find the coordinates of T.

a. (–2.5, –4.5) b. (0, –2)

c. (0, 0.5) d. (2.5, 0.5)

e. (2.5, –2)

ANSWER: d

POINTS: 1


HAS VARIABLES: True



64. Write the standard form of the equation of the circle with center (5, –7) and radius 5.

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1


HAS VARIABLES: True



65. Write the standard form of the equation of the circle with center (3, –2) and solution point (–2, 3).



a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1


HAS VARIABLES: True



66. Write the standard form of the equation of the circle which has (–5, 4) and (–1, 8) as endpoints of a diameter.

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1


HAS VARIABLES: True



67. Write the standard form of the equation of the circle tangent to the y-axis and with center (–3, –6).

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1


HAS VARIABLES: True



68. Find the center and radius of the circle with equation .

a. Center: (7, 2)

Radius: 5

b. Center: (–7, 2)

Radius: 25

c. Center: (7, –2)

Radius: 25

d. Center: (7, –2)

Radius: 5

e. Center: (–7, 2)



Radius: 5

ANSWER: e

POINTS: 1


HAS VARIABLES: True



69. The point A has coordinates (–3, 5). If A is moved 3 units upward 6 units to the left, what are the new coordinates of A ?

a. (0, –1) b. (3, 8)

c. (0, 11) d. (–9, 8)

e. (3, 2)

ANSWER: d

POINTS: 1


HAS VARIABLES: True



Section 1.2 - Graphs of Equations


1. Determine which of the following point lies on the graph of the equation.

a. (2, 10)

b. (2, 9)

c. (2, 8)

d. (9, 8)

e. (3, 8)

ANSWER: c

POINTS: 1

REFERENCES: 1.1.7


HAS VARIABLES: True




y = |x – 2| + 4

a. (5, 7)

b. (5, 9)

c. (5, 8)

d. (8, 7)

e. (6, 7)

ANSWER: a

POINTS: 1

REFERENCES: 1.1.11


HAS VARIABLES: True



3. Write the standard form of the equation of the circle with the given characteristics.

Endpoints of a diameter: (2, 2), (12, 2)

a.

b.

c.

d.



e.

ANSWER: e

POINTS: 1

REFERENCES: 1.1.68


HAS VARIABLES: True




Center:(3, 1); Radius: 7

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 1.1.63


HAS VARIABLES: True



5. Find the center and radius of the circle, and sketch its graph.

a. Centre (0, 0), Radius 16



b. Centre (0, 0), Radius 4

c. Centre (0, 0), Radius 4



d. Centre (0, 0), Radius 16

e. Centre (0, 0), Radius 4



ANSWER: c

POINTS: 1

REFERENCES: 1.1.69


HAS VARIABLES: True



6. Find the center and radius of the circle, and sketch its graph.

a.

Centre , Radius



b.

Centre , Radius

c.

Centre , Radius

d.

Centre , Radius



e.

Centre , Radius

ANSWER: e

POINTS: 1

REFERENCES: 1.1.73


HAS VARIABLES: True



7. Identify any intercepts and test for symmetry. Then sketch the graph of the equation.

y = x2 – 4x

a. x-intercept : (0, 0), (4, 0)



y-intercept : (0, 0)

No symmetry

b. x-intercept : (0, 0), (–4, 0)


No symmetry

c. x-intercept : (4, 0), (4, 0)


No symmetry



d. x-intercept : (0, 0), (4, 0)


No symmetry

e. x-intercept : (0, 0), (4, 0)

y-intercept : (0, –1)

No symmetry



ANSWER: a

POINTS: 1

REFERENCES: 1.1.39


HAS VARIABLES: True




Center: (6, 1); Solution point: (5, 9)

a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 1.1.66


HAS VARIABLES: True





9. Complete the table. Use the resulting solution points to sketch the graph of the equation. y = –2x + 3

x

–1

0

1

4

y

(x, y)

a.

x –1 0 1 4

y 5 3 1 –5 –6

(x, y) (–1, 5) (0, 3) (1, 1) (4, –5) ( , 9)

b.

x –1 0 1 4

y 5 3 1 –5 –6

(x, y) (–1, 5) (0, 1) (1, 3) (4, –5) ( , –6)



c.

x –1 0 1 4

y 5 3 1 –5 –6

(x, y) (5, –1) (3, 0) (1, 1) (4, –5) ( , –6)

d.

x –1 0 1 4

y 5 3 1 –5 –6

(x, y) (–1, 5) (3, 0) (1, 1) (4, –5) ( , –6)



e.

x –1 0 1 4

y 5 3 1 –5 –6

(x, y) (–1, 5) (0, 3) (1, 1) (4, –5) ( , –6)

ANSWER: e

POINTS: 1

REFERENCES: 1.1.15


HAS VARIABLES: True





10. Graphically estimate the x- and y-intercepts of the graph.

y = |x + 3|

a. x-intercept: (–3, 0)

y-intercept: (0, 3)

b. x-intercept: (0, –3)

y-intercept: (3, 0)

c. x-intercept: (0, –3)

y-intercept: (0, 3)

d. x-intercept: (3, 0)

y-intercept: (3, 0)

e. x-intercept: (0, 3)

y-intercept: (3, 0)

ANSWER: a

POINTS: 1

REFERENCES: 1.1.21


HAS VARIABLES: True






a. (3, 1)

b. (2, 3)

c. (4, 1)

d. (2, 1)

e. (2, 2)

ANSWER: d

POINTS: 1

REFERENCES: 1.1.13


HAS VARIABLES: True



12. Which of the following graphs are symmetric about the y-axis?

a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 1.1.28


HAS VARIABLES: True



13. You purchase an all-terrain vehicle (ATV) for $2,000. The depreciated value y after t years

is given by y = 2,000 – 500t, 0 ≤ t ≤ 6. Sketch the graph of the equation.

a.



b.

c.



d.

e.



ANSWER: a

POINTS: 1

REFERENCES: 1.1.76


HAS VARIABLES: True



14. The resistance y (in ohms) of 1,000 feet of solid copper wire at 68 degrees Fahrenheit can be approximated by the model

where x is the diameter of the wire in mils (0.001 inch). Complete the table.

x 15 45 55 70 75

y

Round the answer to two decimal places. a.

x 15 45 55 70 75

y 47.50 1.54 3.19 1.83 4.95

b.

x 15 45 55 70 75

y 47.50 4.95 3.19 1.54 1.83

c.

x 15 45 55 70 75

y 47.50 4.95 1.83 3.19 1.54



d.

x 15 45 55 70 75

y 47.50 3.19 4.95 1.83 1.54

e.

x 15 45 55 70 75

y 47.50 4.95 3.19 1.83 1.54

ANSWER: e

POINTS: 1

REFERENCES: 1.1.80


HAS VARIABLES: True



15. A hospital purchases a new magnetic resonance imaging (MRI) machine for $600,000. The depreciated value y (reduced value)after t years is given by y = 600,000 – 20,000t, 0 ≤ t ≤ 6. Sketch the graph of the equation.

a.

b.



c.

d.



e.

ANSWER: c

POINTS: 1

REFERENCES: 1.1.75


HAS VARIABLES: True




a. (6, 0)

b. (7, 6)



c. (7, 6)

d. (6, 7)

e. (6, 8)

ANSWER: a

POINTS: 1

REFERENCES: 1.1.14


HAS VARIABLES: True



17. Complete the table.

x –12 –8 4 12 16

y

(x,y)

a.

x –12 –8 4 12 16

y –10 –7 2 8 11

(x,y) (–10, –12) (–7, –8) (4, 2) (12, 8) (16, 11)

b.

x –12 –8 4 12 16

y –10 –7 2 8 11

(x,y) (–12, –10) (–8, –7) (2, 4) (12, 8) (11, 16)

c. x –12 –8 4 12 16

y –10 –7 2 8 11

(x,y) (–12, –10) (–7, –8) (2, 4) (12, 8) (16, 11)

d. x –12 –8 4 12 16

y –10 –7 2 8 11

(x,y) (–12, –10) (–8, –7) (4, 2) (12, 8) (16, 11)

e. x –12 –8 4 12 16

y –10 –7 2 8 11

(x,y) (–12, –10) (–8, 2) (4, –7) (12, 8) (16, 11)

ANSWER: d

POINTS: 1

REFERENCES: 1.1.16




HAS VARIABLES: True




a. x-intercept: (0, 1)

y-intercept: (0, 3)

b. x-intercept: (1, 0)

y-intercept: (3, 0)

c. x-intercept: (0, 1)

y-intercept: (3, 0)


y-intercept: (0, 3)


y-intercept: (0, –3)

ANSWER: d

POINTS: 1

REFERENCES: 1.1.23


HAS VARIABLES: True






y = |x – 4|

a. x- intercept: (4, 0)

y- intercept: (0, 4)

No symmetry

b. x- intercept: (-4, 0)


No symmetry

c. x- intercept: (4, 0)


No symmetry



d. x- intercept: (4, 0)


No symmetry

e. x- intercept: (4, 0)


No symmetry



ANSWER: d

POINTS: 1

REFERENCES: 1.1.45


HAS VARIABLES: True




y = 2 – |x|

a. x- intercept: (±2, 0)


y-axis symmetry



b. x- intercept: (-2, 0)


y-axis symmetry

c. x- intercept: (2, 0)

y- intercept: (0, ±2)

y-axis symmetry

d. x- intercept: (2, 0)


y-axis symmetry



e. x- intercept: (-2, 0)


y-axis symmetry

ANSWER: a

POINTS: 1

REFERENCES: 1.1.46


HAS VARIABLES: True




a. x-intercept: (2, 0)



y-intercept: none

No symmetry


y-intercept: none

No symmetry

c. x-intercept: (2, 0)

y-intercept: (0, )

No symmetry



d. x-intercept: (-2, 0)

y-intercept: none

No symmetry

e. x-intercept: (-2, 0)

y-intercept: none

No symmetry



ANSWER: b

POINTS: 1

REFERENCES: 1.1.43


HAS VARIABLES: True



22. Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts.

a. Intercepts: (0, 7), (-14, 0)

b. Intercepts: (-14, 0), (0, -7)



c. Intercepts: (14, 0), (0, -7)

d. Intercepts: (0, 8), (15, 0)



e. Intercepts: (14, 0), (0, 7)

ANSWER: e

POINTS: 1

REFERENCES: 1.1.49


HAS VARIABLES: True




y = |x + 2|

a. Intercepts: (0, -2), (0, 2)



b. Intercepts: (-2, 0), (0, -2)

c. Intercepts: (2, 0), (0, 2)



d. Intercepts: (-2, 0), (0, 2)

e. Intercepts: (-2, 0), (2, 0)



ANSWER: d

POINTS: 1

REFERENCES: 1.1.59


HAS VARIABLES: True




a. Intercepts: (0, 0), (-2, 0)

b. Intercepts: (0, 0), (2, 0)



c. Intercepts: (0, 0), (-2, 0)

d. Intercepts: (0, 0), (-2, 0)



e. Intercepts: (0, 0), (6, 0)

ANSWER: c

POINTS: 1

REFERENCES: 1.1.57


HAS VARIABLES: True




y = 3 – |x – 1|

a. (4, 2)

b. (6, 0)

c. (5, 0)



d. (4, 0)

e. (4, 1)

ANSWER: d

POINTS: 1

REFERENCES: 1.1.10


HAS VARIABLES: True



26. Complete the table. Use the resulting solution points to sketch the graph of the equation.

x 4 5 –5 –2 –3

y

(x,y)

x 4 5 –5 –2 –3

y

(x,y)

x 4 5 –5 –2 –3

y

(x,y)

a.

x 4 5 –5 –2 –3

y –11 –20 –20 1 –4

(x,y) (4, –11) (–20,5) (–20, –5) (–2, 1) (–3, –4)



b.

x 4 5 –5 –2 –3

y –11 –20 –20 1 –4

(x,y) (4, –11) (5, –20) (–5, –20) (–2, 1) (–3, –4)

c.

x 4 5 –5 –2 –3

y –11 –20 –20 1 –4

(x,y) (4, –11) (5, –20) (–5, –20) (–2, 1) (–3, –4)



d.

x 4 5 –5 –2 –3

y –11 –20 –20 1 –4

(x,y) (4, –11) (5, –20) (–20, –5) (–2, 1) (–4, –3)

e.

x 4 5 –5 –2 –3

y –11 –20 –20 1 –4

(x,y) (–11, 4) (–20, 5) (–5, –20) (–2, 1) (–3, –4)



ANSWER: b

POINTS: 1

REFERENCES: 1.1.18


HAS VARIABLES: True






a. x-intercept: (±3, 0)

y-intercept: (0, 81)



c. x-intercept: (-3, 0)


d. x-intercept: (±3, 0)

y-intercept: (0, 9)



ANSWER: a

POINTS: 1

REFERENCES: 1.1.20


HAS VARIABLES: True






a. x-intercept: (±1, 0), (0, 0)

y-intercept: (0, 0)

b. x-intercept: (1, 0), (0, 0)

y-intercept: (0, 0)

c. x-intercept: (-1, 0), (0, 0)

y-intercept: (0, 0)

d. x-intercept: (0, ±1), (0, 0)

y-intercept: (0, 0)

e. x-intercept: (0, 1), (0, 0)

y-intercept: (0, 0)

ANSWER: a

POINTS: 1

REFERENCES: 1.1.24


HAS VARIABLES: True




a. x- intercept: ( , 0)


No symmetry



b. x- intercept: ( , 0)

y- intercept: (0, -6)

No symmetry

c. x- intercept: ( , 0)


No symmetry



d. x- intercept: ( , 0)


No symmetry

e. x- intercept: ( , 0)


No symmetry



ANSWER: b

POINTS: 1

REFERENCES: 1.1.42


HAS VARIABLES: True



30. Assume that the graph has y-symmetry. Select the complete graph of the equation.

a.



b.

c.



d.

e.



ANSWER: a

POINTS: 1

REFERENCES: 1.1.33


HAS VARIABLES: True



31. Assume that the graph has Origin symmetry. Select the complete graph of the equation.

a. b.



c.

d.

e.



ANSWER: a

POINTS: 1

REFERENCES: 1.1.35


HAS VARIABLES: True




a. x-intercept : none


The graph has y-symmetry.



b. x-intercept : (0, 0), (-3, 0)


No symmetry

c. x-intercept : (0, 0), (-3, 0)


No symmetry

d. x-intercept : (0, 0), (3, 0)


No symmetry



e. x-intercept : (0, 0), (3, 0)


No symmetry

ANSWER: a

POINTS: 1

REFERENCES: 1.1.41


HAS VARIABLES: True






a.

Intercepts: (-2, 0), (2, 0), (0, 4)

b.

Intercepts: (-2, 0), (0, -4)

c.

Intercepts: (-2, 0), (2, 0), (0, -



4)

d.

Intercepts: (2, 0), (0, -4)

e.

Intercepts: (2, 0), (0, 4)

ANSWER: c

POINTS: 1

REFERENCES: 1.1.51


HAS VARIABLES: True




a.



Intercepts: (0, 0), (-2,

0)

b.

Intercepts: (0, 0)

c.



Intercepts: (0, 0), (2, 0)

d.

Intercepts: (2, 0), (0, 0)

e.

Intercepts: (-2, 0), (0,



0)

ANSWER: c

POINTS: 1

REFERENCES: 1.1.52


HAS VARIABLES: True



35. Determine which point lies on the graph of the equation .

a. (0, -10)

b. (1, -10)

c. (0, -12)

d. (2, -11)

e. (1, -12)

ANSWER: a

POINTS: 1

REFERENCES: 1.1.9a


HAS VARIABLES: True



36. Determine which point does not lie on the graph of the equation . a. (-2, -15)

b. (-4, -17)

c. (7, -10)

d. (4, -6)

e. (0, -13)

ANSWER: d

POINTS: 1

REFERENCES: 1.1.10a


HAS VARIABLES: True



37. Create and complete a table to find the x and y coordinates of points that lie on the graph of the equation below. Plot at least 5 points along with the graph of the equation.



a.

b.

c.

d.



e.

ANSWER: b

POINTS: 1

REFERENCES: 1.1.15


HAS VARIABLES: True



38. Find the x- and y-intercepts of the graph of the equation .

a. x-intercept:


b.

x-intercept:


c. x-intercept: (–7, 0)


d. x-intercept:

y-intercept: none

e. x-intercept:

y-intercept: (0, 7)

ANSWER: e

POINTS: 1

REFERENCES: 1.1.21


HAS VARIABLES: True






a. x-intercept:

y-intercept:

b.

x-intercept:

y-intercept:

c. x-intercept:

y-intercept:

d. x-intercept:

y-intercept:

e. x-intercept:

y-intercept:

ANSWER: b

POINTS: 1

REFERENCES: 1.1.22


HAS VARIABLES: True



40. Use algebraic tests to check the following for symmetry with respect to the axes and the origin.

a. Symmetric with respect to the origin.

b. No symmetry.

c. Symmetric with respect to the y-axis.

d. Symmetric with respect to the x-axis.

ANSWER: d

POINTS: 1

REFERENCES: 1.1.26


HAS VARIABLES: True





41. Use algebraic tests to check the following for symmetry with respect to the axes and the origin.

a. No symmetry.

b. Symmetric with respect to the y-axis.

c. Symmetric with respect to the origin.

d. Symmetric with respect to the x-axis.

ANSWER: b

POINTS: 1

REFERENCES: 1.1.28


HAS VARIABLES: True



42. Assume the graph has the indicated type of symmetry. Sketch the complete graph.

symmetric with respect to the origin.



a.

b.

c.

d.

e.

ANSWER: b



POINTS: 1

REFERENCES: 1.1.35


HAS VARIABLES: True



43. Find the x- and y-intercepts of the graph of the equation y = 36 – 6x. a. x-intercept: (6, 0)

y-intercept: (0, -6)


y-intercept: (0, 6)

c. x-intercept: (-6, 0)

y-intercept: (0, -36)





ANSWER: e

POINTS: 1

REFERENCES: 1.1.22


HAS VARIABLES: True




a. x-intercept:

y-intercept: none

b. x-intercept:

y-intercept:

c. x-intercept:

y-intercept: none

d. x-intercept:

y-intercept:

e. x-intercept:

y-intercept: none

ANSWER: e

POINTS: 1



REFERENCES: 1.1.19


HAS VARIABLES: True



45. Write the standard form of the equation of the circle with the given characteristics. center: (–1, –5); radius: 6

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 1.1.63


HAS VARIABLES: True



46. Write the standard form of the equation of the circle with the given characteristics. center: (–5, –4); solution point: (–3, –7)

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 1.1.65


HAS VARIABLES: True



47. Write the standard form of the equation of the circle with the given characteristics. endpoints of a diameter: (3, 4), (7, 8)



a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 1.1.68


HAS VARIABLES: True



48. Find the center and radius of the circle .

a. center: (0, 0), radius: 11

b. center: (-1, 1), radius: 11

c. center: (0, 0), radius: 7

d. center: (-1, -1), radius: 7

e. center: (–7, –11), radius: 7

ANSWER: c

POINTS: 1

REFERENCES: 1.1.69


HAS VARIABLES: True



49. Find the center and radius of the circle .

a. center: (1, 5), radius 5

b. center: (5, 1), radius 25

c. center: (–5, –1), radius 5

d. center: (–5, –1), radius 25

e. center: (5, 1), radius 5

ANSWER: e

POINTS: 1

REFERENCES: 1.1.71


HAS VARIABLES: True





50. You purchase a house for $250,000. The depreciated value, y, after x years is given by y = 250,000 – 12,500x. Sketch the graph of the equation given 0 ≤ x ≤ 8.

a.

b.

c.

d.



e.

ANSWER: a

POINTS: 1

REFERENCES: 1.1.76


HAS VARIABLES: True



51. Find the graph of the equation.

f (x) = | x – 2 |

a.

b.



c.

d.

ANSWER: d

POINTS: 1


HAS VARIABLES: True




a.

b.



c.

d.

ANSWER: b

POINTS: 1


HAS VARIABLES: True



53. Find the value of y that corresponds to x = –4 in the graph of the equation 2x + 3y = 13.

a. 9

b. –7

c. –9

d. 21

e. 7

ANSWER: e

POINTS: 1


HAS VARIABLES: True



54. Find the value of x that corresponds to y = 7 in the graph of the equation 4x – 3y = –37.

a. 4

b. –16

c. –3

d. 3

e. –4

ANSWER: e

POINTS: 1




HAS VARIABLES: True



55. Find the y-intercept of the graph of the equation y = 3x + 18.

a. (0, 3)

b. (18, 0)

c. (-6, 0)

d. (0, 18)

e. (0, -6)

ANSWER: d

POINTS: 1


HAS VARIABLES: True



56. Find the x-intercept of the graph of the equation y = 3x + 15.

a. (0, -5)

b. (0, 15)

c. (15, 0)

d. (0, 3)

e. (-5, 0)

ANSWER: e

POINTS: 1


HAS VARIABLES: True



57. Find the y-intercept of the graph of the equation 4y = 3x + 12.

a. (0, -3)

b. (-4, 0)

c. (0, 3)

d. (0, -4)

e. (0, 12)

ANSWER: c

POINTS: 1


HAS VARIABLES: True





58. Sketch the graph of the equation .

a.

b.

c.

d.



e.

ANSWER: d

POINTS: 1


HAS VARIABLES: True



59. Sketch the graph of the equation y = 4|x – 3| + 2.

a.

b.



c.

d.

e.

ANSWER: e

POINTS: 1


HAS VARIABLES: True



60. Find the x-intercept of the graph of the equation .

a. (0, -6)

b. (0, 6)

c. (6, 0)

d. (-6, 0)

e. (0, -18)

ANSWER: c



POINTS: 1


HAS VARIABLES: True



61. Find any x- or y-intercepts for the graph of the equation .

a. x-intercepts: (0, 12)

y-intercepts: (2, 0), (6, 0)

b. x-intercepts: (-2, 0), (-6, 0)

y-intercepts: (0, 12)

c. x-intercepts: (2, 0), (6, 0)

y-intercepts: none

d. x-intercepts: (0, 2), (0, 6)


e. x-intercepts: (2, 0), (6, 0)


ANSWER: e

POINTS: 1


HAS VARIABLES: True



62. Graph the circle .

a.

b.

c. d.



e. None of the above.

ANSWER: a

POINTS: 1


HAS VARIABLES: True



63. Graph the circle .

a.

b.

c. d.



e.

ANSWER: c

POINTS: 1


HAS VARIABLES: True



Section 1.3 - Linear Equations in Two Variables


1. Estimate the slope of the line.

a. 5.5

b. 3.5

c. 4.5

d. 6.5

e. Undefined

ANSWER: b

POINTS: 1

REFERENCES: 2.1.13


HAS VARIABLES: True



2. Find the slope and y-intercept (if possible) of the equation of the line. Select the correct answer for the line.



a.

m = –8

y-intercept: (0, 1)

b.

m = –1

y-intercept: (0, 1)

c.

m is undefined. y-intercept: (0, 1)

d.

m = 1

y-intercept: (0, 1)



e.

m = 8

y-intercept: (0, 1)

ANSWER: e

POINTS: 1

REFERENCES: 2.1.17


HAS VARIABLES: True




a.

b.



m = –1

y-intercept: (0, 3)

m = 1


c.


d.

m = 3

y-intercept: (0, 3)

e.



m = –3


ANSWER: b

POINTS: 1

REFERENCES: 2.1.18


HAS VARIABLES: True



4. Find the slope and y-intercept (if possible) of the equation of the line. Select the line.



a.

m = –6

y-intercept: (0, 6)

b.


c.

y-intercept: (0, 6)

d.

m = –1

y-intercept: (0, 6)



e.

m = 6

y-intercept: (0, 6)

ANSWER: c

POINTS: 1

REFERENCES: 2.1.19


HAS VARIABLES: True






a.

m is undefined. There is no y-intercept.

b.

m = –3

y-intercept: (0, 5)

c.


d.

m = –5

y-intercept: (0, 3)

e.




ANSWER: a

POINTS: 1

REFERENCES: 2.1.21


HAS VARIABLES: True






a.

m = 0


b.

m = 0

There is no y-intercept.

c.

m = –6

y-intercept: (0, 3)

d.

m = –3

y-intercept: (0, 6)

e.



m is undefined. y-intercept: (0, –2)

ANSWER: a

POINTS: 1

REFERENCES: 2.1.22


HAS VARIABLES: True






a.

m = –3


b.

m = 0

y-intercept: (0, 3)

c.


d.

m = 0


e.



m = 0


ANSWER: b

POINTS: 1

REFERENCES: 2.1.25


HAS VARIABLES: True






a.

m = 0

y-intercept: (0,4)

b.

m = 0

y-intercept: (0,–4)

c.


d.

m = 0

y-intercept: (0,–4)



e.

m = 0


ANSWER: d

POINTS: 1

REFERENCES: 2.1.26


HAS VARIABLES: True






a.

m = –3

y-intercept: (0,2)

b.


c.

m = –2

y-intercept: (0,3)

d.


e.




ANSWER: e

POINTS: 1

REFERENCES: 2.1.27


HAS VARIABLES: True



10. Find the slope of the line passing through the given pair of points.

(0, 9), (2, 0)



a.

m = –

b.

m =

c.

m = –

d.

m =



e.

m = –

ANSWER: c

POINTS: 1

REFERENCES: 2.1.29


HAS VARIABLES: True



11. Find the slope of the line passing through the pair of points.

(14, 0), (0, –3)



a.

m =

b.

m =

c.

m =

d.

m = –



e.

m = –

ANSWER: c

POINTS: 1

REFERENCES: 2.1.30


HAS VARIABLES: True




(–1, –8), (3, 7)



a.

m =

b.

m =

c.

m = –

d.

m = –



e.

m =

ANSWER: b

POINTS: 1

REFERENCES: 2.1.31


HAS VARIABLES: True




(8, –4), (1, –4)



a.

m = 0

b.

m = –

c.

m =

d.

m is undefined



e.

m =

ANSWER: a

POINTS: 1

REFERENCES: 2.1.33


HAS VARIABLES: True




(10, 12), (12, –12)



a.

m = –12

b.

m = –12

c.

m =

d.

m =



e.

m =

ANSWER: b

POINTS: 1

REFERENCES: 2.1.32


HAS VARIABLES: True




(0, –8), (–6, 0)



a.

m =

b.

m =

c.

m = –

d.

m =



e.

m = –

ANSWER: e

POINTS: 1

REFERENCES: 2.1.36


HAS VARIABLES: True




(4.1, 3.1), (–3.8, 3.1)



a.

m = 0.40

b.

m = –Infinity

c.

m = 0.80

d.

m = 0.00



e.

m = 20.67

ANSWER: d

POINTS: 1

REFERENCES: 2.1.39


HAS VARIABLES: True



17. Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m. Select correct answer for the line.

P(0, –7), m = 8

a.

b.



c.

d.

e.



ANSWER: d

POINTS: 1

REFERENCES: 2.1.51


HAS VARIABLES: True




a.

b.



c.

d.

e.



ANSWER: c

POINTS: 1

REFERENCES: 2.1.53


HAS VARIABLES: True




a.

b.



c.

d.

e.



ANSWER: e

POINTS: 1

REFERENCES: 2.1.54


HAS VARIABLES: True



20. Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m. Select the correct answer for the line.

P(3, –7), m is undefined.

a.

b.



c.

d.

e.



ANSWER: d

POINTS: 1

REFERENCES: 2.1.59


HAS VARIABLES: True




P(4, ), m = 0

a.

b. y = 4x +



c. y =

d. x = 4y +

e.



ANSWER: c

POINTS: 1

REFERENCES: 2.1.61


HAS VARIABLES: True




P(2.4, –8.7), m = –4

a.

x = 2.4y + 0.9 b.

x = 2.4



c.

y = 2.4

d.

y = –4x + 0.9

e.

y = 2.4x + 0.9



ANSWER: d

POINTS: 1

REFERENCES: 2.1.64


HAS VARIABLES: True



23. Find the slope-intercept form of the equation of the line passing through the points. Select the correct answer for the line.

a. y = x–2

b. y = x–6



c. y = x+2

d. y = x–4

e. y = x+6



ANSWER: c

POINTS: 1

REFERENCES: 2.1.65


HAS VARIABLES: True



24. Find the slope-intercept form of the equation of the line passing through the points. Select the correct answer for the line.

a. y = x+1

b. y = x–6



c. y = x–2

d. y = x–1

e. y = – x–2



ANSWER: d

POINTS: 1

REFERENCES: 2.1.66


HAS VARIABLES: True



25. Determine whether the lines are parallel, perpendicular, or neither.

L1: y = x – 4

L2: y = x – 3

a. Perpendicular

b. Parallel

c. Neither

ANSWER: b

POINTS: 1

REFERENCES: 2.1.79


HAS VARIABLES: True






L1: y = x – 4

L2: y = – x – 2

a. Parallel

b. Perpendicular

c. Neither

ANSWER: c

POINTS: 1

REFERENCES: 2.1.81


HAS VARIABLES: True




L1: y = x – 9

L2: y = – x – 2

a. Perpendicular

b. Neither

c. Parallel

ANSWER: a

POINTS: 1

REFERENCES: 2.1.82


HAS VARIABLES: True



28. Use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is

.

x-intercept: (3, 0)

y-intercept: (0, 9)

a.

b.

c.



d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.1.97


HAS VARIABLES: True




x-intercept: (–3, 0)

y-intercept: (0, 8)

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.1.98


HAS VARIABLES: True




x-intercept:

y-intercept:



a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.1.99


HAS VARIABLES: True




x-intercept: ( , 0)

y-intercept:

a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.1.100


HAS VARIABLES: True




Point on line: (4, 6)

x-intercept: (c, 0)

y-intercept: (0, c), c ≠ 0



a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.1.101


HAS VARIABLES: True



33. Estimate the slope of the line.

a. –2

b. –3

c. –4

d. –1

e. Undefined

ANSWER: c

POINTS: 1

REFERENCES: 2.1.15


HAS VARIABLES: True





34. The following is the slope of line representing annual sale y in term of time x in year. Use the slope to interpret any change in annual sales for a one-year increase in time.

The line has a slope of m = 134.

a. No change in sales

b. Sales decreasing 134 units/yr

c. Sales increasing 134 units/yr

d. None of the above

ANSWER: c

POINTS: 1

REFERENCES: 2.1.111a


HAS VARIABLES: True



35. The following is the slope of line representing annual sale y in term of time x in year. Use the slope to interpret any change in annual sales for a one-year increase in time.

The line has a slope of m = –20.

a. Sales increasing 20 units/yr

b. Sales decreasing 20 units/yr

c. No change in sales


ANSWER: b

POINTS: 1

REFERENCES: 2.1.111c


HAS VARIABLES: True



36. The following is the slope of line representing daily revenue y in term of time x in day. Use the slope to interpret any change in daily revenues for a one-day increase in time.

The line has a slope of m = 500.

a. Revenues increasing 500 units/day

b. No change in revenues

c. Revenues decreasing 500 units/day




ANSWER: a

POINTS: 1



HAS VARIABLES: True



37. The graph shows the average salaries for senior high school principals from 1996 through 2008.

Find the slope of the line segment connecting the points for the years 1998 and 2002.

a. –2394

b. 2391

c. –2391

d. 2396

e. 2392

ANSWER: b

POINTS: 1

REFERENCES: 2.1.113b


HAS VARIABLES: True



38. The graph shows the sales (in billions of dollars) for Apple Inc. for the years 2001 through 2007.



Find the slope of the line segment connecting the points for the years 2003 and 2004. Round the answer to two decimal places.

a. –5.07

b. 2.07

c. 7.07

d. 3.07

e. –2.07

ANSWER: b

POINTS: 1



HAS VARIABLES: True



39. You are driving on a road that has a 5% uphill grade. This means that the slope of the road is .

Approximate the amount of vertical change in your position if you drive 400 feet.

a. 18 ft

b. 21 ft

c. 22 ft

d. 19 ft

e. 20 ft

ANSWER: e

POINTS: 1

REFERENCES: 2.1.115


HAS VARIABLES: True





40. A sub shop purchases a used pizza oven for $885. After 5 years, the oven will have to be replaced. Select the linear equation giving the value V of the equipment during the 5 years it will be in use.

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.1.121


HAS VARIABLES: True



41. A school district purchases a high-volume printer, copier, and scanner for $20,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2,600. Select a linear equation giving the value of the equipment during the 10 years it will be in use.

a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.1.122


HAS VARIABLES: True



42. A discount outlet is offering a 70% discount on all items. Select a linear equation giving the sale price S for an item with a list price L.

a.

b.

c.

d.

e.

ANSWER: e



POINTS: 1

REFERENCES: 2.1.123


HAS VARIABLES: True



43. A microchip manufacturer pays its assembly line workers $12.25 per hour. In addition, workers receive a piecework rate of $0.3 per unit produced. Select a linear equation for the hourly wage W in terms of the number of units x produced per hour.

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.1.124


HAS VARIABLES: True



44. A pharmaceutical salesperson receives a monthly salary of $2600 plus a commission of 2% of sales. Select a linear equation for the sales-person’s monthly wage W in terms of monthly sales S.

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.1.125


HAS VARIABLES: True



45. A sales representative of a company using a personal car receives $160 per day for lodging and meals plus $0.53 per mile driven. Select a linear equation giving the daily cost C to the company in terms of x, the number of miles driven.

a.



b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.1.126


HAS VARIABLES: True



46. A real estate office handles an apartment complex with 60 units. When the rent per unit is $98 per month, all 60 units are occupied. However, when the rent is $630 per month, the average number of occupied units drops to 46. Assume that the relationship between the monthly rent p and the demand x is linear. Select the equation of the line giving the demand x in terms of the rent p.

a. x = 532p + 62.58

b. x = –38p – 62.58

c. x = p + 62.58

d. x = –38p + 62.58

e. x = 14p + 62.58

ANSWER: c

POINTS: 1



HAS VARIABLES: True



47. The length and width of a rectangular garden are 16 meters and 11 meters, respectively. A walkway of width

x surrounds the garden. Write the equation for the perimeter y of the walkway in terms of x.

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1





HAS VARIABLES: True



48. Determine whether the statement is true or false. Justify your answer.

A line with a slope of is steeper than a line with a slope of .

a. True. The slope with the smallest magnitude corresponds to the steepest line.

b. False. The slope with the greatest magnitude corresponds to the steepest line.

ANSWER: b

POINTS: 1

REFERENCES: 2.1.137


HAS VARIABLES: True



49. Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line.

point: (–4, 9) line: 6x - 30y = 6

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.1.87


HAS VARIABLES: True



50. Carl's Tractor Service purchases a used brush mower for $1445. The machine has a useful life of 5 years after which time another one will have to be purchased. Assume depreciation of the machine is linear. Write a linear equation giving the value V of the used brush mower during the 5 years it will be in use.



a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.1.121


HAS VARIABLES: True




P(–4, 3); Q(2, –9).

a. m = 1

b. m = –7

c. m = 4

d. m = –2

e. m = –1

ANSWER: d

POINTS: 1


HAS VARIABLES: True




P(5, 4); Q(9, 20).

a. m = 5

b. m = 4

c. m = 2

d. m = 3

e. m = 6

ANSWER: b

POINTS: 1




HAS VARIABLES: True




P (–9, 14); Q (–18, –2)

a. m =

b. m = –

c. m = –

d. m =

e. none of these

ANSWER: a

POINTS: 1


HAS VARIABLES: True




a. m = 19

b. m = 1

c. m = 2

d. m = -1

e. none of these

ANSWER: d

POINTS: 1


HAS VARIABLES: True



55. Draw the line using the slope and y-intercept.

y + 1 = 2x



a.

b.

c.

d.

ANSWER: d

POINTS: 1


HAS VARIABLES: True



56. Find the slope of the line.

y = 9x + 25



a. m = –9

b. m = 10

c. m = 13

d. m = 9

e. m = 6

ANSWER: d

POINTS: 1


HAS VARIABLES: True



57. Find the y-intercept of the line determined by the equation.

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1


HAS VARIABLES: True



58. Find the slope of the line determined by the equation.

a.

b.

c.



d.

e.

ANSWER: c

POINTS: 1


HAS VARIABLES: True



59. Write the equation of the line that passes through the point P(0, 0) and is parallel to the line y = 8x – 7.

a. x = 8y

b. y = 7x +8

c. y = –7x

d. y = 8x

e. y = 7x

ANSWER: d

POINTS: 1


HAS VARIABLES: True



60. Write the equation of the line that passes through the point P (0, 0) and is perpendicular to the line y = – 2x + 10.

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1


HAS VARIABLES: True



61. Write the equation of the line that passes through the point P(4, 3) and is perpendicular to the line y = – 5x +



2.

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1


HAS VARIABLES: True



62. Find the slope of the line through P(–8, –5) and Q(2, 35).

ANSWER: 4

POINTS: 1

QUESTION TYPE: Numeric Response

HAS VARIABLES: True



63. A line passes through the two points P(3, 3),and Q(–5, –5). Write the equation in slope-intercept form.

ANSWER: y = x

POINTS: 1

QUESTION TYPE: Subjective Short Answer

HAS VARIABLES: True



64. Write the equation of the line that passes through the point P (0, 0), and is parallel to the line y = 8x - 1.

Write the answer in slope-intercept form.

ANSWER: y = 8 · x

POINTS: 1


HAS VARIABLES: True





Tell whether the slope of the line is positive, negative, 0, or undefined. Choose the correct letter for each question.

a.

b.

c.

d.

QUESTION TYPE: Matching

HAS VARIABLES: True



65. undefined slope

ANSWER: d

POINTS: 1

66. negative slope

ANSWER: b

POINTS: 1

67. zero slope

ANSWER: c

POINTS: 1

68. positive slope

ANSWER: a

POINTS: 1

Determine whether the line through the given points and the line through R (8,7) and S(5,14) are parallel, perpendicular, or neither.



Choose the correct letter for each question.

a. P(16, 14); Q(10, 28)

b. P(21, –24); Q(42, –15)

c. P(14, 14); Q(0, –10)





69. perpendicular

ANSWER: b

POINTS: 1

70. neither

ANSWER: c

POINTS: 1

71. parallel

ANSWER: a

POINTS: 1

Section 1.4 - Functions


1. Which set of ordered pairs represents a function from A to B?

A = {3, 2, 4, 1} and B = {–4, –5, 3, 2, 4}

a. {(3, –4), (2, –5), (4, –4), (3, –5)}

b. {(3, –4), (4, 4), (2, –5), (1, 3), (2, 2)}

c. {(3, 4), (1, 3), (2, 2)}

d. {(3, 2), (2, –4), (4, 3), (1, 4)}

e. {(3, –4), (2, 2), (1, 3)}

ANSWER: d

POINTS: 1

REFERENCES: 2.2.15


HAS VARIABLES: True



2. Which set of ordered pairs represents a function from A to B?

A = {a, b, c} and B = {4, 3, 1, 2}

a. {(a, 4), (b, 3)}

b. {(a, 2), (c, 3), (b,4 )}

c. {(a, 4), (c, 1)}

d. {(a, 1), (c, 3), (c, 1), (b, 4)}

e. {(a, 4), (c, 3), (c, 1), (b, 1)}

ANSWER: b

POINTS: 1

REFERENCES: 2.2.16


HAS VARIABLES: True



3. Which of the following equation represents y as a function of x?

a. y2 = 9 – x

b. y3 = x + 9

c. y2 = x + 9

d. x2 + y = 9

e. x2 + y2 = 9

ANSWER: d

POINTS: 1

REFERENCES: 2.2.21




HAS VARIABLES: True



4. Which of the following equation does not represent y as a function of x?

a. y2 = 1 – x

b. y = x2 + 1

c. x2 + y = 1

d. y = x2 + x – 1

e. y = x2 – 1

ANSWER: a

POINTS: 1

REFERENCES: 2.2.27


HAS VARIABLES: True



5. Evaluate f(7) if f(x) = 4x – 1.

a. f(7) = 27

b. f(7) = 26

c. f(7) = 29

d. f(7) = 25

e. f(7) = 28

ANSWER: a

POINTS: 1

REFERENCES: 2.2.37a


HAS VARIABLES: True



6. Evaluate f(–7) if f(x) = 12x – 8.

a. f(–7) = –89

b. f(–7) = –91

c. f(–7) = –88

d. f(–7) = –92

e. f(–7) = –90

ANSWER: d



POINTS: 1

REFERENCES: 2.2.37b


HAS VARIABLES: True



7. Evaluate g(s + 2) if g(y) = 12 – 5y.

a. g(s + 2) = –2 + 5s

b. g(s + 2) = –2 – 5s

c. g(s + 2) = 2 + 5s

d. g(s + 2) = 2 – 5s

e. g(s + 2) = 12 – 5s

ANSWER: d

POINTS: 1

REFERENCES: 2.2.38c


HAS VARIABLES: True



8. Evaluate S(3) if S(r) = 4πr2.

a. S(3) = 40π

b. S(3) = 9π

c. S(3) = 38π

d. S(3) = 36π

e. S(3) = 37π

ANSWER: d

POINTS: 1

REFERENCES: 2.2.40a


HAS VARIABLES: True



9. Evaluate g(t) – g(9) if g(t) = 12t2 – 6t + 3.

a. g(t) – g(9) = 12t2 – 918 + 6t

b. g(t) – g(9) = 6t2 – 918t + 12

c. g(t) – g(9) = 12t2 – 918t – 6

d. g(t) – g(9) = 6t2 + 12t – 918



e. g(t) – g(9) = 12t2 – 6t – 918

ANSWER: e

POINTS: 1

REFERENCES: 2.2.41c


HAS VARIABLES: True



10. Evaluate f(16) if .

a. f(16) = 5

b. f(16) = 7

c. f(16) = 4

d. f(16) = 8

e. f(16) = 6

ANSWER: e

POINTS: 1


HAS VARIABLES: True




a. f(11) = –1

b. f(11) = 2

c. f(11) = 0

d. f(11) = 1

e. f(11) = 3

ANSWER: d

POINTS: 1

REFERENCES: 2.2.47b


HAS VARIABLES: True



12. Evaluate q(4) if .

a. q(4) =



b. q(4) =

c. q(4) =

d. q(4) =

e. q(4) =

ANSWER: c

POINTS: 1

REFERENCES: 2.2.45a


HAS VARIABLES: True




a. f(0) = –9

b. f(0) = 6

c. f(0) = 9

d. f(0) = –6

e. f(0) = 0

ANSWER: c

POINTS: 1

REFERENCES: 2.2.49b


HAS VARIABLES: True



14. Evaluate f(–4) if .

a. f(–4) = 19

b. f(–4) = 11

c. f(–4) = 16

d. f(–4) = 23

e. f(–4) = 21

ANSWER: e

POINTS: 1

REFERENCES: 2.2.50a




HAS VARIABLES: True



15. Evaluate the function at .

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.2.51b


HAS VARIABLES: True



16. Evaluate the function at f(7).

a. f(7) = 61

b. f(7) = 58

c. f(7) = 57

d. f(7) = 59

e. f(7) = 60

ANSWER: c

POINTS: 1

REFERENCES: 2.2.52b


HAS VARIABLES: True






f(x) = x2 – 3

x –3 –1 0 4 5

f(x)

a.

x –3 –1 0 4 5

f(x) 6 –2 13 –3 22

b.

x –3 –1 0 4 5

f(x) 6 –2 –3 22 13

c.

x –3 –1 0 4 5

f(x) –2 6 –3 13 22

d.

x –3 –1 0 4 5

f(x) 6 –2 0 13 22

e.

x –3 –1 0 4 5

f(x) 6 –2 –3 13 22

ANSWER: e

POINTS: 1

REFERENCES: 2.2.53


HAS VARIABLES: True




t –11 –9 0 –5 –1

h(t)

a.

t –11 –9 0 –5 –1

h(t) 3 4 –3 1 1

b.

t –11 –9 0 –5 –1

h(t)

4

3

1

1



c.

t –11 –9 0 –5 –1

h(t)

4

3

1

1

d.

t –11 –9 0 –5 –1

h(t)

4

3

1

1

e.

t –11 –9 0 –5 –1

h(t) 4 3 0 1 1

ANSWER: d

POINTS: 1

REFERENCES: 2.2.55


HAS VARIABLES: True




s

0

4

7

f(s)

a.

s

0

4

7

f(s) –1 1 1 1 1

b.

s

0

4

7

f(s) –1 1 1 3 1

c.



s 0 4

7

f(s) –1 1 3 1 1

d.

s

0

4

7

f(s) 1 1 3 1 1

e.

s

0

4

7

f(s) –1 3 1 1 1

ANSWER: a

POINTS: 1


HAS VARIABLES: True




x –6 –4 0 1 4

f(x)

a.

x –6 –4 0 1 4

f(x) 9 7 –3 1 4

b.

x –6 –4 0 1 4

f(x) 7 6 4 3 6

c.

x –6 –4 0 1 4

f(x) 7 6 4 1 4

d.

x –6 –4 0 1 4

f(x) 7 6 0 1 4

e.

x –6 –4 0 1 4

f(x) 7 8 4 4 1



ANSWER: c

POINTS: 1

REFERENCES: 2.2.57


HAS VARIABLES: True



21. Find all real values of x such that f(x) = 0.

f(x) = 12 – 2x

a. x = 6

b. x = 5

c. x = 7

d. x = 4

e. x = 8

ANSWER: a

POINTS: 1

REFERENCES: 2.2.59


HAS VARIABLES: True



22. Find all real value of x such that f (x) = 0.

a. x =

b. x =

c. x = ±

d. x =

e. x = ±

ANSWER: a

POINTS: 1

REFERENCES: 2.2.61


HAS VARIABLES: True






a. x = ±12

b. x = ±13

c. x = ±11

d. x = ±10

e. x = ±9

ANSWER: e

POINTS: 1

REFERENCES: 2.2.62


HAS VARIABLES: True




f(x) = x2 – 8x – 20

a. x = –10, 2

b. x = –10, –2

c. x = 2, 10

d. x = –2, 10

e. x = –8, 8

ANSWER: d

POINTS: 1

REFERENCES: 2.2.64


HAS VARIABLES: True



25. Find the domain of the function.

f(x) = 2x2 + 4x – 5

a. All real numbers x such that x > 0

b. All real numbers x

c. All real numbers x such that x < 0

d. Non-negative real numbers x

e. Non-negative real numbers x except x = 0



ANSWER: b

POINTS: 1

REFERENCES: 2.2.71


HAS VARIABLES: True




a. All real numbers t except t = 0

b. Negative real numbers t

c. All real numbers t such that t > 0

d. Non-negative real numbers t

e. All real numbers t such that t = 0

ANSWER: a

POINTS: 1

REFERENCES: 2.2.73


HAS VARIABLES: True




a. Non-negative real numbers x except x = 4

b. All real numbers x except x = 0

c. Non-negative real numbers x

d. All real numbers x

e. All real numbers x such that x > 0

ANSWER: e

POINTS: 1

REFERENCES: 2.2.81


HAS VARIABLES: True






a. Non-negative real numbers x

b. All real numbers x

c. All real numbers x such that x > –4

d. Non-negative real numbers x except x =4

e. All real numbers x such that x < 4

ANSWER: c

POINTS: 1

REFERENCES: 2.2.80


HAS VARIABLES: True



29. Assume that the domain of f is the set A = {–5, –3, 0, 3, 5}. Determine the set of ordered pairs that represents

the function f.

f(x) = x2

a. {(–5, 25), (–3, 81), (0, 0), (3, 81), (5, 25)}

b. {(–5, –125), (–3, 9), (0, 0), (3, 9), (5, –125)}

c. {(–5, 25), (–3, –27), (0, 0), (3, –27), (5, 25)}

d. {(–5, 625), (–3, 9), (0, 0), (3, 9), (5, 625)}

e. {(–5, 25), (–3, 9), (0, 0), (3, 9), (5, 25)}

ANSWER: e

POINTS: 1

REFERENCES: 2.2.83


HAS VARIABLES: True




the function f.

f(x) = (x – 3)2

a. {(–4, 49), (–2, 1), (0, 9), (2, 625), (3, 49)}

b. {(–4, –343), (–2, 1), (0, 9), (2, 25), (3, –343)}

c. {(–4, 49), (–2, –125), (0, 0), (2, –125), (3, 49)}

d. {(–4, 2401), (–2, 1), (0, 0), (2, 25), (3, 2401)}

e. {(–4, 49), (–2, 25), (0, 9), (2, 1), (3, 0)}



ANSWER: e

POINTS: 1

REFERENCES: 2.2.84


HAS VARIABLES: True




the function f.

f(x) = |x + 1|

a. {(–5, 4), (–2, 3), (0, 1), (2, 4), (3, 3)}

b. {(–5, 4), (–2, 4), (0, 1), (2, 4), (3, 4)}

c. {(–5, 7), (–2, 3), (0, 1), (2, 1), (3, 7)}

d. {(–5, 4), (–2, 1), (0, 1), (2, 3), (3, 4)}

e. {(–5, 6), (–2, 1), (0, 1), (2, 3), (3, 6)}

ANSWER: d

POINTS: 1

REFERENCES: 2.2.86


HAS VARIABLES: True



32. A rectangle is bounded by the x-axis and the semicircle (see figure). Select the area A of the

rectangle as a function of x, and determine the domain of the function.



a. , –7 ≤ x ≤ 7

b. , –7 ≤ x ≤ 7

c. , x ≥ 0

d. , x ≥ 0

e. , all real numbers

ANSWER: a

POINTS: 1

REFERENCES: 2.2.92


HAS VARIABLES: True




f(x) = x3 – x

2 – 9x + 9

a. x = 0, 3

b. x = 1, –3

c. x = 0, –3

d. x = 1, 3

e. x = 1, ±3

ANSWER: e

POINTS: 1

REFERENCES: 2.2.66


HAS VARIABLES: True



34. Find the difference quotient and simplify your answer.

f(x) = x2 – x + 1, , h ≠ 0

a. , h ≠ 0

b. , h ≠ 0



c. , h ≠ 0

d. , h ≠ 0

e. , h ≠ 0

ANSWER: a

POINTS: 1

REFERENCES: 2.2.103


HAS VARIABLES: True




f(x) = 5x – x2, , h ≠ 0

a. , h ≠ 0

b. , h ≠ 0

c. , h ≠ 0

d. , h ≠ 0

e. , h ≠ 0

ANSWER: d

POINTS: 1

REFERENCES: 2.2.104


HAS VARIABLES: True



36. Does the table describe a function?

Input value 2001 2002 2003 2004 2005

Output value 20 50 20 40 30

a. No

b. Yes

ANSWER: b



POINTS: 1

REFERENCES: 2.2.13


HAS VARIABLES: True




Input value 20 40 20 30 50

Output value 2001 2002 2003 2004 2005

a. Yes

b. No

ANSWER: b

POINTS: 1

REFERENCES: 2.2.14


HAS VARIABLES: True




Input value 5 10 14 10 5

Output value –13 –8 0 8 13

a. Yes

b. No

ANSWER: b

POINTS: 1

REFERENCES: 2.2.11


HAS VARIABLES: True




Input value –5 –3 0 3 5

Output value –3 –3 –3 –3 –3

a. No

b. Yes

ANSWER: b

POINTS: 1

REFERENCES: 2.2.12


HAS VARIABLES: True





40. Which set of ordered pairs represents a function from P to Q?

P = {5, 10, 15, 20} Q = {–1, 1, 3}

a. {(5, 3), (15, 1), (5, –1), (15, 3)}

b. {(15, –1), (15, 1), (15, 3)}

c. {(5, –1), (10, 1), (10, 3), (15, 1), (20, –1)}

d. {(15, 1), (10, –1), (5, 1), (10, 3), (15, –1)}

e. {(5, –1), (10, 1), (15, 3), (20, –1)}

ANSWER: e

POINTS: 1

REFERENCES: 2.2.15


HAS VARIABLES: True



41. Which equation does not represent y as a function of x?

a. 2x = 8y

b. –4y = –8

c. 5x2 + 5y = 3

d. 3x + 6y = –5

e. 7y2 + 8x = 9

ANSWER: e

POINTS: 1

REFERENCES: 2.2.21


HAS VARIABLES: True



42. Which equation does not represent y as a function of x?

a.

b. y = |–2 + 7x2|

c. x = –6y - 2

d. x = –8

e. y = –3x + 5

ANSWER: d

POINTS: 1

REFERENCES: 2.2.33




HAS VARIABLES: True



43. Evaluate the function at the specified value of the independent variable and simplify.

g(s) = 3s + 1

g(–18)

a. g(–18) = –55

b. g(–18) = –54s + 3

c. g(–18) = –18s - 1

d. g(–18) = –18s + 1

e. g(–18) = –53

ANSWER: e

POINTS: 1

REFERENCES: 2.2.38


HAS VARIABLES: True




g( )

a. g( ) =

b. g( ) =

c. g( ) =

d. g( ) = 5

e. g( ) =

ANSWER: e

POINTS: 1


HAS VARIABLES: True






a. x = 2

b. x =

c. x =

d. x =

e. x =

ANSWER: d

POINTS: 1

REFERENCES: 2.2.61


HAS VARIABLES: True



46. Find all real value of x such that f (x) = 0.

f(x) = 64x2 – 36

a. x = ±

b. x = ±

c. x = –

d. x =

e. x = ±

ANSWER: b

POINTS: 1

REFERENCES: 2.2.63


HAS VARIABLES: True



47. Find the value(s) of x for which f (x) = g (x).

f(x) = x2 + x – 13 g(x) = –5x + 3

a. x= –8, 2

b. x= 8, –2



c. x= –13, 1,

d. x= –13, –14,

e. x= 12,

ANSWER: a

POINTS: 1

REFERENCES: 2.2.68


HAS VARIABLES: True




a. w = –6, w = 0

b. w = –6

c. all real numbers w ≠ –6, w ≠ 0

d. all real numbers

e. all real numbers w ≠ –6

ANSWER: e

POINTS: 1

REFERENCES: 2.2.74


HAS VARIABLES: True




f(y) = 6y2 - 3y, , h ≠ 0

a.

b.

c.

d.



e.

ANSWER: a

POINTS: 1

REFERENCES: 2.2.105


HAS VARIABLES: True




q(p) = –6p - 3

q(–2.6)

a. q(–2.6) = 15.6p + 18

b. q(–2.6) = 18.6

c. q(–2.6) = 12.6

d. q(–2.6) = –2.6p - 3

e. q(–2.6) = –2.6p + 3

ANSWER: c

POINTS: 1

REFERENCES: 10


HAS VARIABLES: True




f(y - 5)

a. f(y - 5)=

b. f(y - 5)=

c. f(y - 5)=

d. f(y - 5)=

e. f(y - 5)=



ANSWER: a

POINTS: 1

REFERENCES: 12


HAS VARIABLES: True




a. –9 ≤ p ≤ 9

b. p ≤ –9 or p ≥ 9

c. p ≥ 0

d. p ≤ 9

e. all real numbers

ANSWER: a

POINTS: 1

REFERENCES: 17


HAS VARIABLES: True



53. Let the function be defined by the equation , where and are real numbers. Find the domain

of the function

a. domain:

b.

domain:

c. domain:

d.

domain:

e.

domain:

ANSWER: e

POINTS: 1




HAS VARIABLES: True



54. Let the function f be defined by the equation y = f (x) , where x and f (x) are real numbers. Find the domain

and range of the function .

a. domain:

b. domain:

c. domain:

d.

domain:

e.

domain:

ANSWER: e

POINTS: 1


HAS VARIABLES: True




f (x) = | x - 4 |

a.

b.



c.

d.

ANSWER: d

POINTS: 1


HAS VARIABLES: True



56. Evaluate the difference quotient for the function.

f (x) = 2x - 7

a. –7

b.

c. 7

d. 2x + 7

e. 2

ANSWER: e

POINTS: 1


HAS VARIABLES: True



Indicate whether the equation determines y to be a function of x. Match each equation with the corresponding

answer.


a. y – 2x = 0

b. x = –2







57. yes

ANSWER: a

POINTS: 1

58. no

ANSWER: b

POINTS: 1

Section 1.5 - Analyzing Graphs of Functions


1. Find the zeros of the function algebraically.

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.3.23


HAS VARIABLES: True




a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.3.24


HAS VARIABLES: True






a. x = 5

b. x = 10

c. x = 9

d. x = 8

e. x = 0

ANSWER: e

POINTS: 1

REFERENCES: 2.3.25


HAS VARIABLES: True




a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.3.26


HAS VARIABLES: True




a.

b.

c.



d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.3.27


HAS VARIABLES: True




a. x = 0, 16

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.3.31


HAS VARIABLES: True




a.

b.

c.

d.

e.

ANSWER: a



POINTS: 1

REFERENCES: 2.3.32


HAS VARIABLES: True



8. Select the graph of the function and find the zeros of the function.

a.

b.

c.

d.



e.

ANSWER: e

POINTS: 1

REFERENCES: 2.3.33


HAS VARIABLES: True




a. b.



x = 0, 9

x = –6, 0

c.

x = –6, 0

d.

x = 6

e.



x = 0, 6

ANSWER: e

POINTS: 1

REFERENCES: 2.3.34


HAS VARIABLES: True




a.

b.



c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.3.35


HAS VARIABLES: True



11. Find the average rate of change of the function from x1 = 0 to x2 = 3.



a. The average rate of change from x1 = 0 to x2 = 3 is –2.

b. The average rate of change from x1 = 0 to x2 = 3 is 12.

c. The average rate of change from x1 = 0 to x2 = 3 is 2.

d. The average rate of change from x1 = 0 to x2 = 3 is –12.

e. The average rate of change from x1 = 0 to x2 = 3 is 19.

ANSWER: a

POINTS: 1

REFERENCES: 2.3.75


HAS VARIABLES: True




a. The average rate of change from x1 = 0 to x2 = 3 is –3.


c. The average rate of change from x1 = 0 to x2 = 3 is –10.

d. The average rate of change from x1 = 0 to x2 = 3 is 10.


ANSWER: b

POINTS: 1

REFERENCES: 2.3.76


HAS VARIABLES: True




a. The average rate of change from x1 = 1 to x2 = 5 is 24.

b. The average rate of change from x1 = 1 to x2 = 5 is –4.






ANSWER: a

POINTS: 1

REFERENCES: 2.3.77


HAS VARIABLES: True









ANSWER: b

POINTS: 1

REFERENCES: 2.3.78


HAS VARIABLES: True









ANSWER: b

POINTS: 1

REFERENCES: 2.3.79


HAS VARIABLES: True










e. The average rate of change from x1 = 1 to x2 = 6 is –2.

ANSWER: d

POINTS: 1

REFERENCES: 2.3.80


HAS VARIABLES: True



17. Select the graph of the function and determine whether it is even, odd, or neither.

f(x) = 4

a. Neither

b. Odd

c. Even d. Even



e. Odd

ANSWER: d

POINTS: 1

REFERENCES: 2.3.91


HAS VARIABLES: True




f(x) = 6x – 5

a. b.



Even

Even

c.

Odd

d.

Neither

e.

Odd

ANSWER: d

POINTS: 1

REFERENCES: 2.3.93




HAS VARIABLES: True




f(x) = x2 – 6

a.

Odd

b.

Neither

c.

Odd

d.

Neither

e.



Even

ANSWER: e

POINTS: 1

REFERENCES: 2.3.95


HAS VARIABLES: True




a.

Even

b.

Odd

c. d.



Odd

Even

e.

Neither

ANSWER: e

POINTS: 1

REFERENCES: 2.3.97


HAS VARIABLES: True




a. b.



Even

Odd

c.

Neither

d.

Even

e.

Odd

ANSWER: c

POINTS: 1

REFERENCES: 2.3.98




HAS VARIABLES: True




f(x) = |x + 6|

a.

Even

b.

Odd

c.

Neither

d.

Odd

e.



Even

ANSWER: c

POINTS: 1

REFERENCES: 2.3.99


HAS VARIABLES: True



23. The number of lumens (time rate of flow of light) L from a fluorescent lamp can be approximated by the

model

L = –0.294x2 + 97.744x – 664.875, 20 ≤ x ≤ 90

where x is the wattage of the lamp.

Use a graphing utility to select the graph of the function. Use the graph to estimate the wattage necessary to

obtain 2400 lumens.

a.

40W

b.

30W

c. d.



45W

25W

e.

35W

ANSWER: e

POINTS: 1

REFERENCES: 2.3.109


HAS VARIABLES: True



24. Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the

function is even.

a.



b.

c.

d.

e. None of the above

ANSWER: b

POINTS: 1



HAS VARIABLES: True




function is odd.

a.

b.

c.

d.


ANSWER: a

POINTS: 1



HAS VARIABLES: True




function is even.



(4, 3)

a. (–4, –3)

b. (–4, 3)

c. (4, 3)

d. (4, –3)


ANSWER: b

POINTS: 1



HAS VARIABLES: True




function is odd.

(8, –7)

a. (8, 7)

b. (8, –7)

c. (–8, –7)

d. (–8, 7)


ANSWER: d

POINTS: 1



HAS VARIABLES: True




function is even.

(-x, y)

a. (-x, -y)

b. (x, -y)

c. (-x, y)

d. (x, y)




ANSWER: d

POINTS: 1



HAS VARIABLES: True




function is odd.

(4a, 6b)

a. (–4a, –6b)

b. (–4a, 6b)

c. (4a, –6b)

d. (4a, 6b)


ANSWER: a

POINTS: 1



HAS VARIABLES: True



30. An object is thrown upward from a height of 8 feet at a velocity of 72 feet per second.

Use the position equation s = –16t2 + v0t + s0 to select a function that represents the situation and select the

graph of the function.

a. s = –16t2 – 72t + 8 b. s = –16t

2 + 72t



c. s = –16t2 + 72t – 8

d. s = –16t2 + 72t + 8

e. s = –16t2 – 72t – 8



ANSWER: d

POINTS: 1

REFERENCES: 2.3.115


HAS VARIABLES: True



31. An object is thrown upward from a height of 6.4 feet at a velocity of 80 feet per second.



a. s = –16t2 + 80 – 6.4

b. s = –16t2 + 80t

c. s = –16t2 – 80t – 6.4 d. s = –16t2 – 80t + 6.4



e. s = –16t2 + 80t + 6.4

ANSWER: e

POINTS: 1

REFERENCES: 2.3.116


HAS VARIABLES: True



32. An object is thrown upward from ground level at a velocity of 90 feet per second.





a. s = –16t2 + 90t

b. s = –16t2 – 90t

c. s = 16t2 + 90t

d. s = 16t2 – 90t

e. s = –16t2 + 90t + 8



ANSWER: a

POINTS: 1

REFERENCES: 2.3.117


HAS VARIABLES: True



33. An object is dropped from a height of 60 feet.

Use the position equation s = –16t2 + v0t + s0 to write a function that represents the situation and select the


a. s = 16t2 + 60

b. s = –16t2 – 60

c. s = 16t2 – 60

d. s = –16t2 + 60

e. s = –16t2 + 60t



ANSWER: d

POINTS: 1

REFERENCES: 2.3.119


HAS VARIABLES: True



34. An object is dropped from a height of 15 feet.

Use the position equation s = –16t2 + v0t + s0 to write a function that represents the situation and select the


a. s = –16t2 + 15t

b. s = –16t2 + 15

c. s = –16t2 – 15t

d. s = 16t2 + 15



e. s = –16t2 – 15

ANSWER: b

POINTS: 1

REFERENCES: 2.3.120


HAS VARIABLES: True



35. Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0.

f(x) = 5 – x

a. b.



(∞, –5]

(–∞, –5]

c.

(∞, 5]

d.

(–∞, 5]

e.

(–∞, 5]

ANSWER: e

POINTS: 1



REFERENCES: 2.3.67


HAS VARIABLES: True




f(x) = 16 – x2

a.

[–4, –4]

b.

[–4, 4]

c.

[–4, –4]

d.

[4, –4]

e.



[–4, 4]

ANSWER: e

POINTS: 1

REFERENCES: 2.3.69


HAS VARIABLES: True




a.

(–∞, 2]

b.

[–2, ∞)

c. d.



[–2, 2)

[2, ∞)

e.

[–2, ∞)

ANSWER: d

POINTS: 1

REFERENCES: 2.3.71


HAS VARIABLES: True






a.

f(x) > 6 for all x.

b.

f(x) < 0 for all x.

c.

f(x) ≤ 0 for all x.

d.

f(x) ≥ 0 for all x.

e.



f(x) > 0 for all x.

ANSWER: b

POINTS: 1

REFERENCES: 2.3.73


HAS VARIABLES: True



39. Use the graph of the function to find the domain and range of f.

a. domain: all real numbers

range: (–∞, –1) ∪ (0, ∞)

b. domain: (–∞, –4) ∪ (–4, ∞)

range: (–∞, –1) ∪ (0, ∞)

c. domain: (–∞, –1) ∪ (0, ∞)



range: (–∞, –4) ∪ (–4, ∞)

d. domain: all real numbers

range: (–∞, –1] ∪ [0, ∞)

e. domain: all real numbers

range: all real numbers

ANSWER: b

POINTS: 1

REFERENCES: 2.3.12


HAS VARIABLES: True

LEARNING OBJECTIVES: PREC.LARS.16.117 - Find domain and range of graphs



40. Use the Vertical Line Test to determine in which of the graphs y is not a function of x.

a. All of the choices (A, B, C, and D) represent functions.

b. x2 + y

2 = 16

c.

d.



e.

ANSWER: b

POINTS: 1

REFERENCES: 2.3.17


HAS VARIABLES: True



41. Find the zeroes of the functions algebraically.

a.

b.

c.

d.

e.

ANSWER: b



POINTS: 1

REFERENCES: 2.3.26


HAS VARIABLES: True



42. Find the zeroes of the functions algebraically.

a.

b.

c.

d.

e. no real zeroes

ANSWER: d

POINTS: 1

REFERENCES: 2.3.31


HAS VARIABLES: True



43. Use a graphing utility to graph the function and find the zeroes of the function.

a.

b.

c.

d.

e. no real zeroes

ANSWER: a



POINTS: 1

REFERENCES: 2.3.33


HAS VARIABLES: True



44. Determine the intervals over which the function is increasing, decreasing, or constant.

a. constant on (–∞, 0)

increasing on (0, ∞)

b. increasing on (–∞, 0), (1, ∞)

descreasing on (0, 1)

c. constant on (–∞, 1)


d. constant on (–∞, 1)

descreasing on (1, ∞)

e. constant on (–∞, 0)

descreasing on (0, 1)

ANSWER: b

POINTS: 1

REFERENCES: 2.3.45


HAS VARIABLES: True





45. Use a graphing utility to graph the function and visually determine the intervals over which the function is

increasing, decreasing, or constant.

a. increasing on (–∞, ∞)

b. descreasing on (–∞, 1)


c. increasing on (–∞, 1)

descreasing on (1, ∞)

d. descreasing on (–∞, ∞)

e. descreasing on (1, 1)


ANSWER: b

POINTS: 1

REFERENCES: 2.3.52


HAS VARIABLES: True



46. Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum

or relative maximum values.

a. relative maximum: (2.58, 0.39)

relative minimum: (7.27, –1.72)

b. relative maximum: (0.39, 2.58)

relative minimum: (–1.72, 7.27)

c. relative maximum: (–1.72, 7.27)

relative minimum: (0.39, 2.58)

d. relative maximum: (7.27, –1.72)


e. relative maximum: (2.58, 28.33)


ANSWER: c

POINTS: 1

REFERENCES: 2.3.50


HAS VARIABLES: True



47. Graph the function and determine the interval(s) for which f (x) ≥ 0.



a.

b.

c.

d. {–2}

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.3.70


HAS VARIABLES: True



48. Determine whether the function is even, odd, or neither.

a. neither

b. even

c. odd

ANSWER: a

POINTS: 1

REFERENCES: 2.3.95




HAS VARIABLES: True

LEARNING OBJECTIVES: PREC.LARS.16.121 - Identify even and odd functions



49. Write the height h of the rectangle as a function of x.

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.3.103


HAS VARIABLES: True



50. Use the position equation s = –16t2 + v0t + s0 to write a function that represents the situation and give the average

velocity of the object from time t1 to time t2.

An object is thrown upward from a height of 38 feet at a velocity of 84 feet per second.

t1 = 1, t2 = 3

a. s = –16t2 + 38t + 84; avg. velocity = 79 ft/s

b. s = –16t2 + 84t + 38; avg. velocity = 125 ft/s

c. s = –16t2 + 38t + 84; avg. velocity = –26 ft/s

d. s = –16t2 + 84t + 38; avg. velocity = 20 ft/s



e. s = –16t2 + 84t + 38; avg. velocity = 40 ft/s

ANSWER: d

POINTS: 1

REFERENCES: 2.3.115


HAS VARIABLES: True




a.

b.

c.

d.

ANSWER: b

POINTS: 1


HAS VARIABLES: True





52. Tell where the function is decreasing.

a.

b.

c. always increasing

d. always constant

e. always decreasing

ANSWER: b

POINTS: 1


HAS VARIABLES: True



53. The graph of a function is sketched below.



Determine the interval on which the function is decreasing.

a. (–∞, –3] ∩ [–1, ∞)

b. [–3, –1]

c. [–1, –1]

d. [1, 3]

e. (–∞, –3] ∩ [–1, ∞)

ANSWER: b

POINTS: 1


HAS VARIABLES: True



54. Tell where the function is decreasing.



a. always increasing

b. always decreasing

c. (0, ∞)

d. always constant

e. (–∞, 0)

ANSWER: e

POINTS: 1


HAS VARIABLES: True



55. Graph the piecewise-defined function.

a.

b.



c.

d.

ANSWER: d

POINTS: 1


HAS VARIABLES: True



56. Graph the function.

a.

b.

c. d.



ANSWER: a

POINTS: 1


HAS VARIABLES: True



57. The graph of the function is sketched as follows:

Determine the interval where the function is increasing.

ANSWER:

POINTS: 1


HAS VARIABLES: True



Section 1.6 - A Library of Parent Functions


1. Identify the following function.

a. Constant function

b. Absolute value function

c. Square root function

d. Squaring function

e. Identity function

ANSWER: a

POINTS: 1

REFERENCES: 2.4.1e


HAS VARIABLES: True



2. Select the linear function such that it has the indicated function values.

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.4.11a


HAS VARIABLES: True




a.

b.

c.

d.

e.

ANSWER: a



POINTS: 1

REFERENCES: 2.4.14a


HAS VARIABLES: True




a. f(x) = –x

b. f(x) = 2

c. f(x) = –2

d. f(x) = 4

e. f(x) = x

ANSWER: c

POINTS: 1

REFERENCES: 2.4.15a


HAS VARIABLES: True



5. Select the correct graph of the given function.

a.

b.



c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.4.19


HAS VARIABLES: True






a.

b.

c.

d.

e.

ANSWER: c



POINTS: 1

REFERENCES: 2.4.20


HAS VARIABLES: True




a.

b.

c.

d.

e.



ANSWER: d

POINTS: 1

REFERENCES: 2.4.21


HAS VARIABLES: True




a.

b.



c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.4.23


HAS VARIABLES: True




a. b.



c.

d.

e.



ANSWER: c

POINTS: 1

REFERENCES: 2.4.24


HAS VARIABLES: True




a.

b.

c. d.



e.

ANSWER: c

POINTS: 1

REFERENCES: 2.4.25


HAS VARIABLES: True




a. b.



c.

d.

e.



ANSWER: b

POINTS: 1

REFERENCES: 2.4.27


HAS VARIABLES: True




a.

b.

c. d.



e.

ANSWER: a

POINTS: 1

REFERENCES: 2.4.28


HAS VARIABLES: True




a.

b.



c.

d.

e.



ANSWER: b

POINTS: 1

REFERENCES: 2.4.29


HAS VARIABLES: True



14. Select the correct graph for the given function.

a.

b.



c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.4.30


HAS VARIABLES: True



15. Select the correct graph for the given function.

a. b.



c.

d.

e.



ANSWER: d

POINTS: 1

REFERENCES: 2.4.31


HAS VARIABLES: True




a.

b.

c. d.



e.

ANSWER: b

POINTS: 1

REFERENCES: 2.4.32


HAS VARIABLES: True




a. b.



c.

d.

e.



ANSWER: a

POINTS: 1

REFERENCES: 2.4.34


HAS VARIABLES: True




a.

b.

c. d.



e.

ANSWER: e

POINTS: 1

REFERENCES: 2.4.35


HAS VARIABLES: True




a. b.



c.

d.

e.



ANSWER: a

POINTS: 1

REFERENCES: 2.4.36


HAS VARIABLES: True




a.

b.

c. d.



e.

ANSWER: c

POINTS: 1

REFERENCES: 2.4.37


HAS VARIABLES: True




a. b.



c.

d.

e.



ANSWER: a

POINTS: 1

REFERENCES: 2.4.38


HAS VARIABLES: True




a.

b.

c. d.



e.

ANSWER: e

POINTS: 1

REFERENCES: 2.4.39


HAS VARIABLES: True




a. b.



c.

d.

e.



ANSWER: e

POINTS: 1

REFERENCES: 2.4.40


HAS VARIABLES: True




a.

b.

c. d.



e.

ANSWER: a

POINTS: 1

REFERENCES: 2.4.41


HAS VARIABLES: True




a. b.



c.

d.

e.



ANSWER: e

POINTS: 1

REFERENCES: 2.4.42


HAS VARIABLES: True



26. Evaluate the function f(x) = [[x]] for x = 9.2.

a. f(x) = 2

b. f(x) = 10

c. f(x) = 9

d. f(x) = –9

e. f(x) = 11

ANSWER: c

POINTS: 1

REFERENCES: 2.4.43a


HAS VARIABLES: True



27. Evaluate the function h(x) = 2[[x]] for x = –4.

a. h(x) = –8

b. h(x) = –6

c. h(x) = 4

d. h(x) = –4

e. h(x) = –2



ANSWER: a

POINTS: 1

REFERENCES: 2.4.44a


HAS VARIABLES: True



28. Evaluate the function h(x) = [[x + 9]] for x = –4.

a. h(x) = 13

b. h(x) = 5

c. h(x) = 9

d. h(x) = –13

e. h(x) = –5

ANSWER: b

POINTS: 1

REFERENCES: 2.4.45


HAS VARIABLES: True



29. Evaluate the function f(x) = 2[[x]] + 7 for x = –7.

a. f(x) = –21

b. f(x) = 2

c. f(x) = –2

d. f(x) = –7

e. f(x) = 7

ANSWER: d

POINTS: 1

REFERENCES: 2.4.46


HAS VARIABLES: True



30. Evaluate the function f(x) = [[3x + 1]] for x = 4.

a. f(x) = –4

b. f(x) = 4

c. f(x) = 11

d. f(x) = 13



e. f(x) = 12

ANSWER: d

POINTS: 1

REFERENCES: 2.4.47


HAS VARIABLES: True



31. Evaluate the function for x = 6.

a. h(x) = 9

b. h(x) = 3

c. h(x) = –12

d. h(x) = 12

e. h(x) = –3

ANSWER: d

POINTS: 1

REFERENCES: 2.4.48


HAS VARIABLES: True



32. Evaluate the function f(x) = 3[[3x – 1]] + 5 for x = 6.

a. f(x) = 51

b. f(x) = –6

c. f(x) = 56

d. f(x) = 6

e. f(x) = 46

ANSWER: c

POINTS: 1

REFERENCES: 2.4.49


HAS VARIABLES: True



33. Select the graph of the function f(x) = 3[[x]].



a.

b.

c.

d.

e.



ANSWER: a

POINTS: 1

REFERENCES: 2.4.52


HAS VARIABLES: True



34. Select the graph of the function: f(x) = [[x]] – 4.

a.

b.

c. d.



e.

ANSWER: d

POINTS: 1

REFERENCES: 2.4.53


HAS VARIABLES: True



35. Select the graph of the function: f(x) = [[x + 3]].

a. b.



c.

d.

e.



ANSWER: a

POINTS: 1

REFERENCES: 2.4.55


HAS VARIABLES: True



36. Select the graph of the function f(x) = [[x – 4]].

a.

b.

c.

d.



e.

ANSWER: b

POINTS: 1

REFERENCES: 2.4.56


HAS VARIABLES: True



37. Select the graph of the function.



a.

b.

c.

d.

e.



ANSWER: d

POINTS: 1

REFERENCES: 2.4.57


HAS VARIABLES: True




a.

b.

c. d.



e.

ANSWER: a

POINTS: 1

REFERENCES: 2.4.62


HAS VARIABLES: True




a. b.



c.

d.

e.



ANSWER: e

POINTS: 1

REFERENCES: 2.4.63


HAS VARIABLES: True




a. b.



c.

d.

e.



ANSWER: a

POINTS: 1

REFERENCES: 2.4.64


HAS VARIABLES: True



41. The cost of sending an overnight package from Los Angeles to Miami is $26.30 for a package weighing up to but not including 1 pound and $4.00 for each additional pound or portion of a pound. A model for the total cost C (in dollars) of sending the package is

С = 26.30 + 4.00[[x]], x > 0, where x is the weight in pounds.

Select the graph of the model.

a. b.



c.

d.

e.



ANSWER: d

POINTS: 1

REFERENCES: 2.4.69a


HAS VARIABLES: True



42. The cost of sending an overnight package from Los Angeles to Miami is $26.40 for a package weighing up to but not including 1 pound and $3.25 for each additional pound or portion of a pound. A model for the total cost C (in dollars) of sending the package is

С = 26.40 + 3.25[[x]] , x > 0, where x is the weight in pounds.

Determine the cost of sending a package that weighs 5.25 pounds.

a. $45.65

b. $44.65

c. $43.65

d. $46.65

e. $42.65

ANSWER: e

POINTS: 1

REFERENCES: 2.4.69b


HAS VARIABLES: True



43. The cost of sending an overnight package from Los Angeles to Miami is $25.00 for a package weighing up to but not including 1 pound and $3.50 for each additional pound or portion of a pound. Use the greatest integer



function to create a model for the cost C of overnight delivery of a package weighing x pounds, x > 0.

a. C = 25.00 – 3.50[[x]], x > 0

b. C = 25.00 + 3.50[[x]], x > 0

c. C = -25.00 + 3.50[[x]], x > 0

d. С = –25.00 – 3.50 [[x]], x > 0

e. C = 25.00[[x]] + 3.50, x > 0

ANSWER: b

POINTS: 1

REFERENCES: 2.4.70a


HAS VARIABLES: True



44. A mechanic is paid $13.00 per hour for regular time and time-and-a-half for overtime. The weekly wage function is given by

where h is the number of hours worked in a week.

Evaluate W(30), W(50).

a. W(30) = 410, W(50) = 750

b. W(30) = 430, W(50) = 770

c. W(30) = 400, W(50) = 740

d. W(30) = 390, W(50) = 730

e. W(30) = 420, W(50) = 760

ANSWER: d

POINTS: 1

REFERENCES: 2.4.71a


HAS VARIABLES: True



45. The table shows the monthly revenue y (in thousands of dollars) of a landscaping business for each month of the year 2008, with x = 1 representing January.

x y

1 6.0

2 6.1

3 7.1

4 9.2

5 12.3



6 16.4

7 12.2

8 10.2

9 8.3

10 6.3

11 4.3

12 2.4

A mathematical model that represents these data is:

Find f (1) and f (12).

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.4.73b


HAS VARIABLES: True



46. Write the linear function f such that it has the indicated values. f (–1) = –5, f (–9) = –6

a. y = x+

b. y = 8 x+ 3

c. y = x

d. y = x

e. y = x

ANSWER: d

POINTS: 1

REFERENCES: 2.4.12


HAS VARIABLES: True





47. Evaluate the function for the indicated values.

f (x) = 5[[x + 3]] - 5

(i) f (3) (ii) f (–63.30) (iii) f ( )

a. (i) 25 (ii) –305 (iii) 15

b. (i) 25 (ii) –305 (iii) 10

c. (i) 26 (ii) –310 (iii) 15

d. (i) 26 (ii) –310 (iii) 10

e. (i) 25 (ii) –310 (iii) 10

ANSWER: e

POINTS: 1

REFERENCES: 2.4.46


HAS VARIABLES: True



48. Which function does the graph represent?

a. g(x) = [[3x]]

b. g(x) = [[x+3]]

c. g(x) = 3[[x]]

d. g(x) = [[–4x]]

e. g(x) = [[x–3]]

ANSWER: b

POINTS: 1

REFERENCES: 2.4.55




HAS VARIABLES: True



49. Which graph represents the function?

a.

b.

c.

d.



e.

ANSWER: c

POINTS: 1

REFERENCES: 35


HAS VARIABLES: True



50. Which graph represents the function?

a.

b.

c. d.



e.

ANSWER: e

POINTS: 1

REFERENCES: 2.4.58


HAS VARIABLES: True



Section 1.7 - Transformations of Functions


1. For following function, select (on the same set of coordinate axes) a graph for .

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.5.7a




HAS VARIABLES: True




a.

b.

c.

d.

e.



ANSWER: c

POINTS: 1

REFERENCES: 2.5.8b


HAS VARIABLES: True




a.

b.

c. d.



e.

ANSWER: e

POINTS: 1

REFERENCES: 2.5.7b


HAS VARIABLES: True



4. For following function, select (on the same set of coordinate axes) a graph of function for .

a. b.



c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.5.10a


HAS VARIABLES: True





5. Use the given graph of f to select the graph for the following function.

a.

b.

c.

d.

e.



ANSWER: d

POINTS: 1

REFERENCES: 2.5.11f


HAS VARIABLES: True



6. Use the given graph of f to select the graph for the following function.

y = f(2x)

a. b.



c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.5.12g


HAS VARIABLES: True





7. Use the given graph of f to select the graph for following function.

a.

b.

c.

d.

e.



ANSWER: d

POINTS: 1

REFERENCES: 2.5.13d


HAS VARIABLES: True



8. Use the given graph of f to select the graph for following function.

a. b.



c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.5.14c


HAS VARIABLES: True





9. Use the graph of to write an equation for the function whose graph is shown.

a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.5.15a


HAS VARIABLES: True






a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.5.15c


HAS VARIABLES: True




a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.5.16a


HAS VARIABLES: True






a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.5.16b


HAS VARIABLES: True






a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.5.17a


HAS VARIABLES: True




a.

b.



c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.5.17d


HAS VARIABLES: True




a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.5.18a


HAS VARIABLES: True






a.

b.

c.

d.


ANSWER: b

POINTS: 1

REFERENCES: 2.5.18c


HAS VARIABLES: True



17. Identify the parent function and the transformation shown in the graph. Write an equation for the function

shown in the graph.

a. Horizontal shift of



b. Vertical shift of

c. Vertical shift of

d. Horizontal shift of

e. Vertical shift of

ANSWER: a

POINTS: 1

REFERENCES: 2.5.19


HAS VARIABLES: True




shown in the graph.

a. Horizontal shift of the x-axis of

b. Vertical shift of the y-axis of

c. Reflection in the x-axis of

d. Horizontal shift of the y-axis of

e. Vertical shift of the x-axis of

ANSWER: c

POINTS: 1

REFERENCES: 2.5.21


HAS VARIABLES: True






shown in the graph.

a. Reflection in the x-axis and vertical shift of

b. Vertical shift of x-axis and vertical shift of

c. Reflection in the x-axis and vertical shift of

d. Horizontal shift of x-axis and vertical shift of

e. Horizontal shift of x-axis and vertical shift of

ANSWER: a

POINTS: 1

REFERENCES: 2.5.23


HAS VARIABLES: True




shown in the graph.



a. Reflection in the x-axis of

b. Horizontal shift of x-axis of

c. Reflection in the y-axis of

d. Horizontal shift of x-axis of

e. Reflection in the y-axis of

ANSWER: b

POINTS: 1

REFERENCES: 2.5.24


HAS VARIABLES: True



21. Identify the parent function f. The parent function is related to g.

a. Absolute Value Function,

b. Constant Function,

c. Identity Function,

d. Quadratic Function,

e. Cubic Function,

ANSWER: d

POINTS: 1

REFERENCES: 2.5.25a


HAS VARIABLES: True





22. The parent function is related to g. Describe the sequence of transformations from f to g.

a. Reflection in the y-axis and vertical shift units upward.

b. Vertical shift of the x-axis and vertical shift units upward.

c. Reflection in the x-axis and vertical shift units upward.

d. Reflection in the x-axis and vertical shift units downward.

e. Reflection in the y-axis and vertical shift units downward.

ANSWER: c

POINTS: 1

REFERENCES: 2.5.25b


HAS VARIABLES: True



23. Select the graph of g.

a.

b.

c. d.



e.

ANSWER: a

POINTS: 1

REFERENCES: 2.5.26c


HAS VARIABLES: True



24. The parent function is related to g. Use function notation to write g in terms of f.

a.

b.

c.

d.

e.

ANSWER: e



POINTS: 1

REFERENCES: 2.5.27d


HAS VARIABLES: True



25. Function is related to the parent function. Identify the parent function f.

a. Identity Function,

b. Cubic Function,

c. Absolute Value Function,

d. Quadratic Function,

e. Constant Function,

ANSWER: b

POINTS: 1

REFERENCES: 2.5.28a


HAS VARIABLES: True




a.

b.

c. d.



e.

ANSWER: c

POINTS: 1

REFERENCES: 2.5.29c


HAS VARIABLES: True




a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1



REFERENCES: 2.5.31d


HAS VARIABLES: True




a. Square Root Function,

b. Identity Function,

c. Quadratic Function,

d. Cubic Function,

e. Reciprocal Function,

ANSWER: a

POINTS: 1

REFERENCES: 2.5.35a


HAS VARIABLES: True




a.

b.

c.

d.


ANSWER: c

POINTS: 1

REFERENCES: 2.5.37d


HAS VARIABLES: True






a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.5.39c




HAS VARIABLES: True




a. Reflection in the y-axis and vertical shift units downward.

b. Reflection in the x-axis and vertical shift units downward.

c. Reflection in the x-axis and vertical shift units upward.

d. Reflection in the y-axis and vertical shift units upward.

e. Vertical shift of the x-axis and vertical shift units downward.

ANSWER: b

POINTS: 1

REFERENCES: 2.5.41b


HAS VARIABLES: True




a. Reciprocal Function,

b. Quadratic Function,

c. Absolute Value Function,

d. Cubic Function,

e. Constant Function,

ANSWER: c

POINTS: 1

REFERENCES: 2.5.43a


HAS VARIABLES: True






a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.5.45d


HAS VARIABLES: True



34. Function g is related to the parent function. Identify the parent function f.

a. Quadratic Function,

b. Greatest Integer Function,

c. Constant Function,

d. Square Root Function,

e. Absolute Value Function,

ANSWER: b

POINTS: 1

REFERENCES: 2.5.47a


HAS VARIABLES: True




a. Horizontal stretch and vertical shift units downward.

b. Vertical shift units to the right.

c. Vertical stretch units to the left.

d. Horizontal stretch and vertical shift units upward.

e. Horizontal shift units to the right.

ANSWER: e



POINTS: 1

REFERENCES: 2.5.49b


HAS VARIABLES: True




a.

b.

c.

d.

e.



ANSWER: d

POINTS: 1

REFERENCES: 2.5.51c


HAS VARIABLES: True




a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.5.53d


HAS VARIABLES: True





38. Write an equation for the function that is described by the given characteristic.

The shape of , but shifted three units to the right and five units downward.

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.5.55


HAS VARIABLES: True




The shape of , but shifted 17 units to the right.

a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.5.57


HAS VARIABLES: True




The shape of , but shifted three units to the left and reflected in both the x-axis and the y-axis.

a.



b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.5.61


HAS VARIABLES: True




a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.5.63a


HAS VARIABLES: True






a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.5.65b


HAS VARIABLES: True




shown in the graph.



a. Vertical stretch of

b. Horizontal stretch of

c. Vertical stretch of

d. Vertical stretch of

e. Horizontal stretch of

ANSWER: c

POINTS: 1

REFERENCES: 2.5.67


HAS VARIABLES: True




shown in the graph.



a. Reflection in the y-axis and vertical shrink of .

b. Reflection in the y-axis and vertical shrink of .

c. Reflection in the y-axis and vertical shrink of .

d. Reflection in the y-axis and vertical shrink of .

e. Reflection in the y-axis and vertical shrink of .

ANSWER: a

POINTS: 1

REFERENCES: 2.5.71


HAS VARIABLES: True



45. Use the viewing window shown to select a possible equation for the transformation of the parent function.

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.5.75




HAS VARIABLES: True



46. Determine whether the statement is true or false. Justify your answer.

The graphs of and are identical.

a. False.

b. True.

ANSWER: b

POINTS: 1

REFERENCES: 2.5.83


HAS VARIABLES: True




a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.5.17


HAS VARIABLES: True

LEARNING OBJECTIVES: PREC.LARS.16.128 - Write equations for transformations of common functions





48. Describe the sequence of transformations from the related common function to g.

a. Vertical shift 4 units up; then vertical shrink by a factor of 2.

b. Horizontal shift 4 units left; then vertical shrink by a factor of 2.

c. Horizontal shift 4 units right; then vertical stretch by a factor of 2.

d. Vertical shift 4 units down; then vertical shrink by a factor of 2.

e. Horizontal shift 4 units left; then vertical stretch by a factor of 2.

ANSWER: c

POINTS: 1

REFERENCES: 2.5.26


HAS VARIABLES: True

LEARNING OBJECTIVES: PREC.LARS.16.129 - Recognize transformed graphs of common functions



49. Write an equation for the function that is described by the following characteristics.

The shape of , but moved five units down, four units to the left, and then reflected in the x-axis.

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.5.58


HAS VARIABLES: True




50. Write an equation for the function that is described by the following characteristics.

The shape of f(x) = [[x]], but reflected in the y-axis, moved eight units down.



a. g(x) = [[–x]] + 8

b. g(x) = –[[x – 8]]

c. g(x) = –[[x + 8]]

d. g(x) = [[–x]] – 8

e. g(x) = –[[x]] + 8

ANSWER: d

POINTS: 1

REFERENCES: 2.5.60


HAS VARIABLES: True





a. Horizontal shift 8 units right; then vertical stretch by a factor of 2.

b. Horizontal shift 8 units left; then vertical stretch by a factor of 2.

c. Horizontal shift 8 units left; then vertical shrink by a factor of 2.

d. Vertical shift 8 units up; then vertical shrink by a factor of 2.

e. Vertical shift 8 units down; then vertical shrink by a factor of 2.

ANSWER: a

POINTS: 1

REFERENCES: 42


HAS VARIABLES: True





a. Reflection in the x-axis; then vertical shift 3 units down.

b. Reflection in the x-axis; then vertical shift 3 units up.

c. Reflection in the y-axis; then vertical shift 3 units up.

d. Reflection in the y-axis; then horizontal shift 3 units right.

e. Reflection in the y-axis; then horizontal shift 3 units left.

ANSWER: b



POINTS: 1

REFERENCES: 43


HAS VARIABLES: True




Section 1.8 - Combinations of Functions: Composite Functions


1. Find (f + g)(x).

a. 2x

b. 4x

c. –4x

d. –2x

e. 2x + 8

ANSWER: a

POINTS: 1

REFERENCES: 2.6.9a


HAS VARIABLES: True



2. Find (f - g)(x).

a. 2x - 6

b. 6

c. 2x - 3

d. 2x + 6

e. 2x

ANSWER: b

POINTS: 1

REFERENCES: 2.6.9b


HAS VARIABLES: True



3. Find (f + g)(x).

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1



REFERENCES: 2.6.10a


HAS VARIABLES: True



4. Find (f - g)(x).

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.6.10b


HAS VARIABLES: True



5. Find (fg)(x).

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.6.11c


HAS VARIABLES: True



6. Find (f / g)(x). What is the domain of f / g?



a.

; all real numbers x.

b. ; all real numbers x except x = 0

c.

; all real numbers x except x =

d. ; all real numbers x except x = 0

e.

; all real numbers x except x =

ANSWER: c

POINTS: 1

REFERENCES: 2.6.11d


HAS VARIABLES: True



7. Find (f + g)(x).

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.6.13a


HAS VARIABLES: True



8. Find .



a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.6.13b


HAS VARIABLES: True



9. Find .

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.6.15c


HAS VARIABLES: True



10. Find .



a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.6.15d


HAS VARIABLES: True



11. Evaluate the indicated function for and .

a. 12

b. –10

c. 7

d. 14

e. 10

ANSWER: e

POINTS: 1

REFERENCES: 2.6.17


HAS VARIABLES: True




a. 28

b. 38



c. –38

d. 125

e. 17

ANSWER: b

POINTS: 1

REFERENCES: 2.6.18


HAS VARIABLES: True




a. 48

b. 39

c. 9

d. 0

e. –39

ANSWER: c

POINTS: 1

REFERENCES: 2.6.19


HAS VARIABLES: True




a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.6.21




HAS VARIABLES: True




a. 92

b. 90

c. –86

d. 89

e. 91

ANSWER: b

POINTS: 1

REFERENCES: 2.6.23


HAS VARIABLES: True




a. 30

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.6.25


HAS VARIABLES: True






a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.6.27


HAS VARIABLES: True



18. Find .

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.6.37a


HAS VARIABLES: True



19. Find .



a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.6.37b


HAS VARIABLES: True



20. Find .

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.6.37c


HAS VARIABLES: True



21. Find and the domain of the composite function.

a.

Domain of : all real numbers x

b.




c.


d.


e.


ANSWER: b

POINTS: 1

REFERENCES: 2.6.41a


HAS VARIABLES: True




a.


b.


c.


d.


e.


ANSWER: c

POINTS: 1

REFERENCES: 2.6.43b


HAS VARIABLES: True






a.


b.


c.


d.


e.


ANSWER: c

POINTS: 1

REFERENCES: 2.6.45a


HAS VARIABLES: True




a.


b.


c.


d.


e.


ANSWER: d

POINTS: 1

REFERENCES: 2.6.45b


HAS VARIABLES: True






a.

Domain of : all real numbers x except

b.


c.


d.


e.


ANSWER: c

POINTS: 1

REFERENCES: 2.6.47a


HAS VARIABLES: True




a.


b.


c.




d.


e.


ANSWER: c

POINTS: 1

REFERENCES: 2.6.47b


HAS VARIABLES: True



27. The research and development department of an automobile manufacturer has determined that when a driver is required to stop quickly to avoid an accident, the distance (in feet) the car travels during the driver’s reaction

time is given by , where x is the speed of the car in miles per hour. The distance (in feet) traveled

while the driver is braking is given by . Find the function that represents the total stopping distance

T.

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.6.61a


HAS VARIABLES: True



28. A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet)



of the outer ripple is , where t is the time in seconds after the pebble strikes the water. The area of the

circle is given by the function . Find and interpret .

a. ; represents the area of the circle at time t.

b. ; represents the area of the circle at time t.

c. ; represents the area of the circle at time t.

d. ; represents the area of the circle at time t.

e. ; represents the area of the circle at time t.

ANSWER: d

POINTS: 1

REFERENCES: 2.6.71


HAS VARIABLES: True



29. From 2003 through 2008, the sales (in thousands of dollars) for one of two restaurants owned by the same parent company can be modeled by

where t = 3 represents 2003. During the same six-year period, the sales (in thousands of dollars) for the second restaurant can be modeled by

Write a function that represents the total sales of the two restaurants owned by the same parent company.

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.6.62a


HAS VARIABLES: True





30. The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models

and

where t represents the year, with t = 0 corresponding to 2000.

Find and interpret .

a. , which represents the total number of Navy and Marines

personnel combined.

b. , which represents the total number of Navy and Marines

personnel combined.

c. , which represents the total number of Navy and Marines

personnel combined.

d. , which represents the total number of Navy and Marines

personnel combined.

e. , which represents the total number of Navy and Marines

personnel combined.

ANSWER: d

POINTS: 1

REFERENCES: 2.6.65a


HAS VARIABLES: True



31. The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models

and

where t represents the year, with t = 0 corresponding to 2000.

Find and interpret .

a. , which represents the difference between the number of

Navy personnel and the number of Marines personnel.

b. , which represents the difference between the number of


c. , which represents the difference between the number of


d. , which represents the difference between the number of




e. , which represents the difference between the number of


ANSWER: e

POINTS: 1

REFERENCES: 2.6.65b


HAS VARIABLES: True



32. The number of people playing tennis T (in millions) in the United States from 2000 through 2007 can be approximated by the function

and the U.S. population P (in millions) from 2000 through 2007 can be approximated by the function

, where t represents the year, with t = 0 corresponding to 2000.

Find .

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.6.66a


HAS VARIABLES: True





33. The number of people playing tennis T (in millions) in the United States from 2000 through 2007 can be approximated by the function

and the U.S. population P (in millions) from 2000 through 2007 can be approximated by the function

, where t represents the year, with t = 0 corresponding to 2000.

Evaluate the function for t = 0 and 3.

a. h(0) = 0.1060, h(3) = 0.0783

b. h(0) = 0.3060, h(3) = 0.2783

c. h(0) = –0.2060, h(3) = –0.1783

d. h(0) = 0.1783, h(3) = 0.2060

e. h(0) = –0.1060, h(3) = –0.0783

ANSWER: a

POINTS: 1

REFERENCES: 2.6.66b


HAS VARIABLES: True



34. The spread of a contaminant is increasing in a circular pattern on the surface of a lake. The radius of the

contaminant can be modeled by , where r is the radius in meters and t is the time in hours since

contamination.

Find a function that gives the area A of the circular lake in terms of the time since the spread began.

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.6.72a


HAS VARIABLES: True



35. The number N of bacteria in a refrigerated food is given by where T is



the temperature of the food in degrees Celsius. When the food is removed from refrigeration, the temperature of

the food is given by where t is the time in hours. Find the bacteria count after 0.5 hour.

a. About 565 bacteria

b. About 793 bacteria

c. About 653 bacteria

d. About 390 bacteria

e. About 705 bacteria

ANSWER: c

POINTS: 1

REFERENCES: 2.6.73b


HAS VARIABLES: True



36. The weekly cost C of producing units x in a manufacturing process is given by . The

number of units x produced in t hours is given by .

Find the cost of the units produced in 6 hours.

a. 11,855

b. 11,850

c. 11,846

d. 13,350

e. 11,854

ANSWER: d

POINTS: 1

REFERENCES: 2.6.74b


HAS VARIABLES: True



37. Determine whether the statement is true or false.

If f(x) = x + 1 and g(x) = 5x, then

.

a. False

b. True

ANSWER: a

POINTS: 1

REFERENCES: 5.6.77




HAS VARIABLES: True



38. The suggested retail price of a new hybrid car is p dollars. The dealership advertises

a factory rebate of $2000 .

Select a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the factory.

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.6.76a


HAS VARIABLES: True



39. Consider the functions and .

Find .

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.6.84a


HAS VARIABLES: True





40. Find (f + g)(x).

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.6.11


HAS VARIABLES: True



41. Find ( f / g )(x).

a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.6.13


HAS VARIABLES: True





42. Find ( fg )(x).

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.6.14


HAS VARIABLES: True




a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.6.21


HAS VARIABLES: True



44. Find ( f − g )(x).



a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.6.16


HAS VARIABLES: True




( fg )(1)

a. 15

b. –35

c. –23

d. –25

e. –33

ANSWER: d

POINTS: 1

REFERENCES: 2.6.23


HAS VARIABLES: True



46. Find .

a.



b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.6.44b


HAS VARIABLES: True



47. Find .

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.6.43a


HAS VARIABLES: True



48. Find .

a.

b.

c.



d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.6.48a


HAS VARIABLES: True



49. Use the graphs of f and g to evaluate the function.

a. 1

b. –2

c. 4

d. –1

e. 2

ANSWER: e

POINTS: 1

REFERENCES: 2.6.52a


HAS VARIABLES: True



50. The monthly cost C of running the machinery in a factory for t hours is given by



The number of hours t needed to produce x products is given by

. Find the equation representing the cost C of manufacturing x products. a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.6.74a


HAS VARIABLES: True



51. Let f (x) = 2x + 1, g(x) = 3x - 2. Find the function.

a.

b.

c.

d.

e. none of the above

ANSWER: b

POINTS: 1





52. Let f (x) = 2x - 1, g(x) = 3x - 2. Find the domain of the function.

a.

b.

c.



d.

e.

ANSWER: a

POINTS: 1


HAS VARIABLES: True



53. Let . Find the composite function which expresses the given correspondence

correctly.

a.

b.

c.

d.


ANSWER: d

POINTS: 1





54. Find .

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1



REFERENCES: 55


HAS VARIABLES: True



55. Let f (x) = x2 - 1, g (x) = 3x - 2. Find the value of the function.

ANSWER: 37

POINTS: 1

QUESTION TYPE: Numeric Response

HAS VARIABLES: True



56. Let f (x) = 2x + 1, g (x) = 3x - 2. Find the function.

Please give the answer as a simplified expression (not an equation).

ANSWER:

POINTS: 1





57. Let . Find the composite function.

ANSWER: |x|

POINTS: 1





58. Let f (x) = 3x, g (x) = x + 1. Find the composite function.

Please give the answer as an expression (not an equation).

ANSWER: 3x + 3

POINTS: 1







Let f (x) = x2 + x, g (x) = x2 - 1. Match the equivalent expressions.


a.

b.





59.

ANSWER: b

POINTS: 1

60.

ANSWER: a

POINTS: 1

Section 1.9 - Inverse Functions


1. Find the inverse function of f informally.

f(x) = 6x

a. f–1(x) = 6 – x

b. f–1(x) = 6 + x

c.

d. f–1(x) = x – 6

e. f(x) = 6x

ANSWER: c

POINTS: 1

REFERENCES: 2.7.7


HAS VARIABLES: True




f(x) = x – 5

a. f–1(x) = – (x + 5)

b.

c.

d. f–1(x) = 5 – x

e. f–1(x) = x + 5

ANSWER: e

POINTS: 1

REFERENCES: 2.7.10


HAS VARIABLES: True




f(x) = x4

a.

b.



c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.7.14


HAS VARIABLES: True



4. Select the correct graph, showing f and g are inverse functions.

a.

b.



c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.7.23b


HAS VARIABLES: True






a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.7.25b


HAS VARIABLES: True






a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.7.27b




HAS VARIABLES: True




a.

b.

c.

d.

e.



ANSWER: e

POINTS: 1

REFERENCES: 2.7.29b


HAS VARIABLES: True




a.

b.

c.

d.



e.

ANSWER: a

POINTS: 1

REFERENCES: 2.7.31b


HAS VARIABLES: True




a.

b.



c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.7.33b


HAS VARIABLES: True



10. Use the tables of values for y = f(x) to complete a table for y = f –1(x).

x –3 –2 0 1 2 3

f(x) –4 –2 2 4 6 8

a.

x –4 –2 2 4 6 8

f –1(x) –3 –2 0 1 8 3

b.

x –4 –2 2 4 6 6

f –1(x) –2 –2 0 1 2 3

c.

x –4 –2 2 4 6 8



f –1(x) –3 0 1 1 8 3

d.

x –4 –2 2 4 6 8

f –1(x) –3 –2 0 6 2 3

e.

x –4 –2 2 4 6 8

f –1(x) –3 –2 0 1 2 3

ANSWER: e

POINTS: 1

REFERENCES: 2.2.37


HAS VARIABLES: True



11. Does the function have an inverse function?

a. No

b. Yes

ANSWER: b

POINTS: 1

REFERENCES: 2.2.39


HAS VARIABLES: True



12. Does the function have an inverse function?



a. No

b. Yes

ANSWER: a

POINTS: 1

REFERENCES: 2.2.41


HAS VARIABLES: True



13. Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function.



a.

The function has an inverse.

b.


c.


d.


e.




ANSWER: a

POINTS: 1

REFERENCES: 2.2.43


HAS VARIABLES: True




g(x) = |x + 5| – |x – 5|

a.

The function does not have inverse.

b.


c. d.





e.


ANSWER: e

POINTS: 1

REFERENCES: 2.2.45


HAS VARIABLES: True




a. b.





c.


d.


e.


ANSWER: c

POINTS: 1

REFERENCES: 2.2.47




HAS VARIABLES: True



16. Select the graph of f and f–1 on the same set of coordinate axes.

f(x) = 2x – 3

a.

b.

c.

d.

e.



ANSWER: a

POINTS: 1

REFERENCES: 2.2.49b


HAS VARIABLES: True



17. Find the inverse function of g(x) = x2 – 3 informally.

a.

b.

c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 2.2..51a


HAS VARIABLES: True



18. Find the inverse function of .

a.

b.



c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.2..53a


HAS VARIABLES: True



19. Select the graph of f and f–1 on the same set of coordinate axes.

a.

b.

c.

d.



e.

ANSWER: a

POINTS: 1

REFERENCES: 2.2.55b


HAS VARIABLES: True



20. Determine whether the function has an inverse function. If it does, find the inverse function.

g(x) = x7

a.

b. g–1(x) = –7x

c.

d. g–1(x) = 7x

e. The inverse exists, but none of the above

ANSWER: e

POINTS: 1

REFERENCES: 2.7.63


HAS VARIABLES: True




a.



b.

c.

d.

e. No inverse

ANSWER: b

POINTS: 1

REFERENCES: 2.7.65


HAS VARIABLES: True




f(x) = –2

a. f–1(x) = 2

b.

c.

d. f–1(x) = –2

e. No inverse

ANSWER: e

POINTS: 1

REFERENCES: 2.7.67


HAS VARIABLES: True




f(x) = (x + 4)2, x ≥ –4

a.

b. f–1(x) = –(x + 4)2

c. f–1(x) = (x + 4)–2

d.

e. No inverse



ANSWER: d

POINTS: 1

REFERENCES: 2.7.69


HAS VARIABLES: True




a.

b.

c.

d.

e. No inverse

ANSWER: e

POINTS: 1

REFERENCES: 2.7.71


HAS VARIABLES: True




a.

b.

c.

d.



e. No inverse

ANSWER: e

POINTS: 1

REFERENCES: 2.7.73


HAS VARIABLES: True




a.

b.

c.

d.

e. No Inverse

ANSWER: c

POINTS: 1

REFERENCES: 2.7.75


HAS VARIABLES: True



27. Restrict the domain of the function f so that the function is one-to-one and has an inverse function. Then find

the inverse function f–1. State the domains and ranges of f and f–1.

f(x) = (x – 5)2

a.

The domain of f and the range of f–1 are all real numbers x such that x ≥ 5.

The domain of f–1 and the range of f are all real numbers x such that x ≥ 0.

b.




The domain of f–1 and the range of f are all real numbers x such that x ≥ –5.

c.



d.



e.

The domain of f and the range of f–1 are all real numbers x such that x ≥ –5.


ANSWER: c

POINTS: 1

REFERENCES: 2.7.77


HAS VARIABLES: True





f(x) = |x + 5|

a. f–1(x) = x – 5



b. f–1(x) = x + 5



c. f–1(x) = x – 5



d. f–1(x) = x + 5





e. f–1(x) = x – 5



ANSWER: a

POINTS: 1

REFERENCES: 2.7.79


HAS VARIABLES: True





f(x) = –6x2 + 2

a.


The domain of f–1 and the range of f are all real numbers x such that x ≤ 2.

b.



c.



d.


The domain of f–1 and the range of f are all real numbers x such that x ≤ –2.

e.





ANSWER: a

POINTS: 1

REFERENCES: 2.7.83


HAS VARIABLES: True





f(x) = |x – 9| + 1

a. f–1(x) = x + 8



b. f–1(x) = x – 8



c. f–1(x) = –x – 8



d. f–1(x) = x + 8



e. f–1(x) = –x + 8



ANSWER: a

POINTS: 1

REFERENCES: 2.7.85


HAS VARIABLES: True



31. Use the functions given by and g(x) = x3 to find (f–1 º g–1)(1).

a. 14

b. 12

c. 16



d. 20

e. 18

ANSWER: c

POINTS: 1

REFERENCES: 2.7.87


HAS VARIABLES: True



32. Use the functions given by and g(x) = x3 to find (g–1 º f–1)(–5).

a. –2

b. 0

c. –4

d. 2

e. 4

ANSWER: b

POINTS: 1

REFERENCES: 2.7.88


HAS VARIABLES: True



33. Use the functions given by and g(x) = x3 to find (f–1 º f–1)(–5).

a. 36

b. 44

c. 40

d. 38

e. 42

ANSWER: c

POINTS: 1

REFERENCES: 2.7.89


HAS VARIABLES: True





34. Use the functions given by and g(x) = x3 to find (f º g)–1.

a.

b.

c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.7.91


HAS VARIABLES: True



35. Use the functions given by and g(x) = x3 to find g–1 º f–1.

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.7.92


HAS VARIABLES: True



36. Use the functions given by f(x) = x + 6 and g(x) = 7x – 3 to find g–1 º f–1.

a.

b.



c.

d.

e.

ANSWER: c

POINTS: 1

REFERENCES: 2.7.93


HAS VARIABLES: True



37. Use the functions given by f(x) = x + 2 and g(x) = 2x – 5 to find (f º g)–1.

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.7.95


HAS VARIABLES: True



38. Your wage is $11.00 per hour plus $0.50 for each unit produced per hour. So, your hourly wage in terms of the number of units produced x is y = 11 + 0.50x. Find the inverse function. What does each variable represent in the inverse function?

a.

x = hourly wage; y = numbers of units produced

b. y = 11 + 0.50x




c.


d.


e. y = 11 – 0.50x


ANSWER: a

POINTS: 1



HAS VARIABLES: True



39. The function given by y = 0.03x2 + 245.50, 0 < x < 100 approximates the exhaust temperature y in degrees

Fahrenheit, x where is the percent load for a diesel engine. Find the inverse function.

a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1






40. Use the graph of the function f to create a table of values for the given points. Then create a second table that

can be used to find f–1.



a.

x 1 4 7 8

y 1 4 7 9

x 1 4 7 9

f–1(x) 1 4 7 8

b.

x 1 4 7 9

y 1 4 7 8

x 1 4 7 8

f–1(x) 1 4 7 9

c.

x 1 4 7 8

y 1 4 7 9

x 1 4 7 9

f–1(x) –1 –4 –7 –8

d.

x –1 –4 –7 –9

y 1 4 7 8

x 1 4 7 8

f–1(x) 1 4 7 9

e.

x –1 –4 –7 –9

y 1 4 7 8

x 1 4 7 9

f–1(x) –1 –4 –7 –8

ANSWER: a

POINTS: 1




HAS VARIABLES: True



41. Consider the functions given by f(x) = x + 3 and f–1(x) = x – 3. Evaluate f(f–1(x)) and f–1(f(x)) for the

indicated values of x. What can you conclude about the functions?

x –1 0 4 49

f(f–1(x))

f–1(f(x))

a.

x –1 0 4 49

f(f–1(x)) –1 0 –4 –49

f–1(f(x)) –1 0 4 49

We can conclude that, both the functions have the same value for negative variables.

b.

x –1 0 4 49

f(f–1(x)) –1 0 4 49

f–1(f(x)) –1 0 4 49

We can conclude that, both the functions have the same value.

c.

x –1 0 4 49

f(f–1(x)) –1 0 4 49

f–1(f(x)) –1 0 –4 –49

We can conclude that, both the functions have the same value for negative variables.

d.

x –1 0 4 49

f(f–1(x)) –1 0 –4 49

f–1(f(x)) –1 0 4 –49

We can conclude that, both the functions are opposite of each other.

e.

x –1 0 4 49

f(f–1(x)) –1 0 4 –49

f–1(f(x)) –1 0 –4 49

We can conclude that, both the functions are opposite of each other.

ANSWER: b

POINTS: 1

REFERENCES: 2.7.114


HAS VARIABLES: True





42. Restrict the domain of f(x) = x2 + 5 to x ≥ 0. Use a graphing utility to graph the function.

a.

b.

c.

d.

e.

ANSWER: a

POINTS: 1

REFERENCES: 2.7.115




HAS VARIABLES: True



43. Find the inverse function of f.

a.

b.

c.

d.

e.

ANSWER: e

POINTS: 1

REFERENCES: 2.7.14


HAS VARIABLES: True



44. Graph the given function.

f(x) = (x – 3)2



a.

b.

c.

d.

e.

ANSWER: b

POINTS: 1

REFERENCES: 2.7.15a


HAS VARIABLES: True






, x ≠

a. , x ≠

b. , x ≠

c. , x ≠ –4

d. , x ≠

e. , x ≠

ANSWER: d

POINTS: 1


HAS VARIABLES: True




f(x) = x2 + 5

a.

b.

c.

d.

e. No inverse function exists.

ANSWER: e

POINTS: 1

REFERENCES: 2.7.63


HAS VARIABLES: True






a.

b.

c.

d.

e. No inverse function exists.

ANSWER: c

POINTS: 1

REFERENCES: 2.7.72


HAS VARIABLES: True



48. Use the functions given by and g(x) = x3 to find the indicated value.

(f º g)–1(5)

a.

b.

c.

d.

e. Undefined

ANSWER: b

POINTS: 1


HAS VARIABLES: True



49. Determine algebraically whether f and g are inverse functions.



f(x) = 5x - 3

a. Yes, f and g are inverse functions.

b. No, f and g are not inverse functions.

ANSWER: a

POINTS: 1

REFERENCES: 2.7.24a


HAS VARIABLES: True



50. Determine algebraically whether f and g are inverse functions.

g(x) = x2 - 6, x ≥ 0

a. Yes, f and g are inverse functions.

b. No, f and g are not inverse functions.

ANSWER: a

POINTS: 1

REFERENCES: 2.7.29a


HAS VARIABLES: True



51. Find the inverse of the one-to-one function.

y = 6x



f –1(x) = __________

ANSWER:

POINTS: 1


HAS VARIABLES: True




f –1(x) = __________

ANSWER:

POINTS: 1


HAS VARIABLES: True




y = 5x + 4

f –1(x) = __________

ANSWER:

POINTS: 1


HAS VARIABLES: True



54. Show algebraically that f and g are inverse functions.

f(x) = 9x + 9

ANSWER:

POINTS: 1



REFERENCES: 58


HAS VARIABLES: True



55. Show algebraically that f and g are inverse functions.

, x ≥ 8 g(x) = x2 + 8, x ≥ 0

ANSWER:

POINTS: 1

REFERENCES: 59


HAS VARIABLES: True



56. Determine whether the function is one-to- one.

y = 3x

a. No, it isn't one-to-one.

b. Yes, it is one-to-one.

ANSWER: b

POINTS: 1


HAS VARIABLES: True



57. Determine whether the function is one-to-one.

y = (x – 5)2; x ≥ 5

a. No, it isn't one-to-one.

b. Yes, it is one-to-one.

ANSWER: b

POINTS: 1


HAS VARIABLES: True






y = 5x + 9

a.

b.

c.

d.


ANSWER: b

POINTS: 1


HAS VARIABLES: True




y = 3x

a.

b. f –1(x) = 3x

c.

d.

e. f –1(x) = 9x

ANSWER: c

POINTS: 1


HAS VARIABLES: True




f(x) = x3 - 4

a.

b.



c.

d.

e.

ANSWER: d

POINTS: 1

REFERENCES: 60


HAS VARIABLES: True



61. The function f(x) = x2 – 2 is one-to-one on the domain (x ≤ 0) . Find f –1(x).

a.

b.

c.

d.

e. f –1(x) = x2 + 2

ANSWER: a

POINTS: 1


HAS VARIABLES: True




a.

b.

c.

d.

e. inverse does not exist

ANSWER: d



POINTS: 1


HAS VARIABLES: True



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